StatPhys Seminar @ UTokyo Hongo
これからのセミナー
2024年7月11日（木）10:30~（第6回）(6th: 10:30-, July 11, 2024)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Leonardo Mazza (Université Paris-Saclay - LPTMS)
Title: ETH, hydrodynamics and quantum scars
Abstract:
The eigenstate thermalization hypothesis is a cornerstone of our
understanding of thermalization in closed quantum many-body systems. In
the first part of the talk I will show that using information on the
hydrodynamic behaviour of the many-body setup it is possible to sharpen
ETH and to derive precise inequalities (often saturated) between the
diagonal and off-diagonal functions postulated in the ETH framework. In
the second part of the talk I will discuss the existence of highly
non-thermal states that can be constructed as non-linear combination of
eigenstates satisfying ETH: they display non-thermal features and relax
on diverging timescales. We dubbed them "asymptotic" quantum many-body
scars.
This seminar is based on the following works:
[1] Gotta, Moudgalya and Mazza, Asymptotic Quantum Many-Body Scars PRL 131, 190401 (2023)
[2] Morettini, Capizzi, Fagotti and Mazza, Energy-filtered quantum states, arXiv:2405.02158 (2024)
[3] Capizzi, Wang, Xu, Mazza and Poletti, Hydrodynamics and the Eigenstate Thermalization Hypothesis, arXiv:2405.16975 (2024)
これまでのセミナー
2024年6月20日（木）10:30~（第5回）(5th: 10:30-, June 20, 2024)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Eva-Maria Graefe (Imperial College London)
Title: (Semi)classical phase-space features of quantum systems with non-Hermitian Hamiltonians
Abstract:
While traditional quantum mechanics focuses on systems conserving energy and probability, described by Hermitian Hamiltonians, in recent decades there has been ever growing interest in the use of non-Hermitian Hamiltonians. These can effectively describe loss and gain in a quantum system. In particular, systems with a certain balance of loss and gain, PT-symmetric systems, have attracted considerable attention. The realisation of PT-symmetric quantum dynamics in optical systems has opened up a whole new field of investigations.
The properties of non-Hermitian quantum systems are often less intuitive than those of conventional Hermitian systems. Here we make use of the Husimi representation in phase space to analyse dynamical and spectral features. We consider the flow of the Husimi phase-space distribution in a semiclassical limit, leading to a first order partial differential equation, that helps illuminate the foundations of the full quantum evolution. Further, we demonstrate how ingredients of the dynamics can be used to construct approximate Husimi distributions of characteristic quantum states.
2024年6月13日（木）10:30~（第4回）(4rd: 10:30-, June 13, 2024)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Yuma Nakanishi (University of Tokyo)
Title: Continuous time crystals originating from PT symmetry and the emergence of critical exceptional point
Abstract:
Continuous time-translation symmetry is often spontaneously broken in open quantum systems, and the condition for their emergence has been actively investigated [1-3]. However, there are only a few cases in which its condition for appearance has been fully elucidated. In this seminar, we show that a Lindladian parity-time (PT) symmetry can generically produce persistent periodic oscillations, including dissipative continuous time crystals, in one-collective spin models [4]. By making an analogy to non-reciprocal phase transitions, we demonstrate that a transition point from the dynamical phase is associated with spontaneous PT symmetry breaking and typically corresponds to a critical exceptional point. These results are established by proving that the Lindbladian PT symmetry at the microscopic level implies a non-linear PT symmetry and by performing a linear stability analysis near the transition point.
[1] F. Iemini, A. Russomanno, J. Keeling, M. Schiro, M. Dalmonte, and R. Fazio, Boundary time crystals,
Phys. Rev. Lett. 21, 35301 (2018).
[2] C. Booker, B. Buca, and D. Jaksch, Non-stationarity and dissipative time crystals: spectral properties and finite-size effects, New J. Phys. 22 085007 (2020).
[3] YN, T. Sasamoto, Dissipative time crystals originating from parity-time symmetry, Phys. Rev. A 107, L010201(2023).
[4] YN, R. Hanai, T. Sasamoto, in preparation.
2024年6月6日（木）10:30~（第3回）(3rd: 10:30-, June 6, 2024)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Hongchao Li (University of Tokyo)
Title: Dissipative Superfluidity in a Molecular Bose-Einstein Condensate
Abstract:
Motivated by recent experimental realization of a Bose-Einstein condensate(BEC) of dipolar molecules, we develop superfluid transport theory for a dissipative BEC to show that a weak uniform two-body loss can induce phase rigidity, leading to superfluid transport of bosons. A generalized f-sum rule is shown to hold for a dissipative superfluid as a consequence of weak U(1) symmetry. In particular, we will show that dissipation enhances the stability of a molecular BEC with dipolar interactions. We also discuss the possible experimental realization.
2024年5月30日（木）10:30~（第2回）(2nd: 10:30-, May. 30, 2024)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Pasquale Marra (University of Tokyo, Keio University)
Title: Majorana modes, topologically nontrivial stripes, and inhomogeneous superconductivity in 2D topological insulator/superconductor heterostructure
Abstract:
Majorana zero modes have garnered significant attention owing to their potential applications in topological quantum computing and the exploration of unconventional quantum phases. These zero-energy states localize at the vortex cores of two-dimensional topological superconductors or at the edges of one-dimensional topological superconducting wires. Their presence is the consequence of the bulk boundary correspondence in the presence of a nontrivial topological state. The braiding of Majorana modes is a noncommutative operation that can be employed to realize a quantum gate, the building block of a topological quantum computer. In our recent work, we introduce an alternative platform: a 2D topological superconductor with inhomogeneous superconductivity, where Majorana modes are localized at the ends of topologically nontrivial 1D stripes. These nontrivial stripes are equivalent to 1D wires and are induced by the spatial variations of the order parameter phase. These Majorana modes are braidable, i.e., their position can be exchanged in space by manipulating the magnetic field.
2024年5月23日（木）10:30~（第1回）(1st: 10:30-, May. 23, 2024)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Masaru Hongo
Title: Relaxation rate of quasi-hydrodynamic mode
Abstract:
Systems with approximate global symmetry support a gapped low-energy mode, which we call a quasi-hydrodynamic mode. The quasi-hydrodynamic mode is a remnant of global symmetry, and has a small but finite relaxation rate. In this talk, I will introduce our ongoing work, in which we are developing a general formulation to describe the quasi-hydrodynamic mode from both phenomenological and statistical mechanical viewpoints. As a result, we obtain a thermodynamic constraint on a source term for an approximate conservation law together with a microscopic (Green-Kubo like) formula to evaluate the relaxation rate.
2024年1月30日（火）10:30~（第11回）(11th: 10:30-, Jan. 30, 2024)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Takato Yoshimura (University of Oxford)
Title: Anomalous relaxation in open quantum circuits
Abstract:
Random matrix theory (RMT) provides a baseline description of spectral statistics in isolated quantum chaotic systems. A standard object that characterises such statistics is the spectral form factor (SFF), which generically shows a late-time ramp and an eventual plateau. In this talk, I will discuss the robustness of such behaviour when a quantum chaotic system is influenced by an environment and quantify it using the dissipative form factor (DFF), which is a dissipative extension of the SFF . To simplify the situation, I will focus on open Floquet many-body systems without conservation laws where the external environment is modelled by quantum channels. It turns out that the competition between quantum chaos and dissipation gives rise to a rich relaxation behaviour of the system. Surprisingly, when the dissipation strength is appropriately scaled and the thermodynamic limit is taken first, the DFF decays with the gap that does not close even in the dissipationless limit.
2023年12月8日（金）10:30~（第10回）(10th: 10:30-, Dec. 8, 2023)
理学部1号館287教室 (Room No. 287, Science 1st Bldg.)
Speaker: Synge Todo
Title: Tensor network and Markov chain Monte Carlo
Abstract:
Many classical and quantum lattice models can be represented as tensor networks [1]. However, the exact contraction of a tensor network is generally exponentially expensive, and some approximation is usually required. In numerical simulations based on the tensor networks, approximations with the singular value decomposition are widely used. On the other hand, various contraction methods based on randomized algorithms have also been proposed (e.g., [2,3,4]). Unfortunately, with naive weighted sampling, controlling the variance is impossible because it diverges exponentially as the network grows.
Here, we propose a new Monte Carlo scheme that combines the stochastic basis transformation of tensors with the Markov-chain Monte Carlo. It can entirely remove the systematic error due to a finite bond dimension of the low-rank approximation in tensor-network contraction while keeping the high accuracy of the tensor-network method. In this talk, we will demonstrate how the proposed method solves the severe sign problems for systems with negative (or complex) weights, such as the unitary evolution in quantum circuits.
[1] J. C. Bridgeman, and C. T. Chubb, J. Phys. A: Math. Theor. 50, 223001 (2017).
[2] A. Sandvik and G. Vidal, Phys. Rev. Lett. 99, 220602 (2007).
[3] L. Wang, I. Pizorn, and F. Verstraete, Phys. Rev. B 83, 134421 (2011).
[4] A. J. Ferris, arXiv:1507.00767.
2023年12月1日（金）10:30~（第9回）(9th: 10:30-, Dec. 1, 2023)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Shoki Sugimoto (The University of Tokyo)
Title: Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems
Abstract:
Recent experimental results have shown the thermalization of isolated quantum systems [1]. However, since the unitary time evolution of such systems preserves the purity of the state, they cannot relax to a mixed state like a thermal ensemble if they are initially in a pure state.
This seems to be a contradiction, but the eigenstate thermalization hypothesis (ETH) [2] provides a solution. According to ETH, every eigenstate of a many-body Hamiltonian is indistinguishable from the microcanonical ensemble regarding physically relevant operators, such as local or few-body ones. The ETH ensures the thermalization of the system from any initial state and has been verified to hold in various nonintegrable systems [3]. Under symmetry, the ETH usually holds within each symmetry sector. However, several numerical studies report that local quantities satisfy the ETH without separating momentum sectors in the presence of translational symmetries [4].
In this talk, we prove an instance of these numerical observations. Namely, we show that local operators satisfy the ETH with the optimal convergence speed in translation invariant spin systems [5]. We prove this fact as a theorem in the full random-matrix regime, where the Hamiltonian contains highly nonlocal and O(N)-body terms, and numerically demonstrate that it generically remains true for locally interacting systems. Our theorem applies to spin systems with arbitrary spin quantum numbers on rectangular lattices of arbitrary dimensions.
[1] A. M. Kaufman et al., Science 353, 794 (2016).
[2] J. M. Deutsch, Phys. Rev. A 43, 2046 (1991). M. Srednicki, Phys. Rev. E 50, 888 (1994).
[3] M. Rigol et al., Nature 452, 854 (2008).
[4] L. Santos and M. Rigol, Phys. Rev. E 82, 031130 (2010).
[5] S. Sugimoto, J. Henheik, V. Riabov, and L. Erdős, J. Stat. Phys. 190, 128 (2023).
2023年11月24日（金）10:30~（第8回）(8th: 10:30-, Nov. 24, 2023)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Hiroshi Shinaoka (Saitama University)
Title: Quantics Tensor Cross Interpolation for High-Resolution, Parsimonious Representations of Multivariate Functions in Physics and Beyond
Abstract:
Multivariate functions of continuous variables arise in countless branches of science. Numerical computations with such functions typically involve a compromise between two contrary desiderata: accurate resolution of the functional dependence, versus parsimonious memory usage. Recently, two promising strategies have emerged for satisfying both requirements: (i) The quantics representation [1,2,3,4,5], which expresses functions as multi-index tensors, with each index representing one bit of a binary encoding of one of the variables; and (ii) tensor cross interpolation (TCI) [6,7,8], which, if applicable, yields parsimonious interpolations for multi-index tensors. In this talk, we present a strategy, quantics TCI (QTCI) [9], which combines the advantages of both schemes. We illustrate its potential with an application from condensed matter physics: the computation of Brillouin zone integrals.
[1] I. V. Oseledets, Doklady Math. 80, 653 (2009).
[2] B. N. Khoromskij, Constr. Approx. 34, 257 (2011).
[3] N. Gourianov et al., Nat. Comput. Sci. 2, 30 (2022).
[4] E. Ye and N. F. G. Loureiro, Phys. Rev. E 106, 035208 (2022).
[5] H. Shinaoka, M. Wallerberger, Y. Murakami, K. Nogaki, R. Sakurai, P. Werner, and A. Kauch, Phys. Rev. X 13, 021015 (2023).
[6] I. V. Oseledets, SIAM Journal on Scientific Computing 33, 2295 (2011).
[7] S. Dolgov and D. Savostyanov, Computer Physics Communications 246, 106869 (2020).
[8] Y. N. Fernandez et al., PRX 12, 041018 (2022).
[9] M. K. Ritter, Y. N. Fernandez, M. Wallerberger, J. von Delft, H. Shinaoka, and X. Waintal, to appear in PRL (arXiv:2303.11819).
2023年11月17日（金）10:30~（第7回）(7th: 10:30-, Nov. 17, 2023)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Kanta Masuki (University of Tokyo)
Title: Cavity QED control of quantum materials
Abstract:
Recent experimental developments in cavity quantum electrodynamics have allowed one to realize strong interaction between light and matter at a single-quantum level. Consequently, the possibility of harnessing cavity confinement as an alternative way to control the phases of matter without an external drive has attracted much attention, which also calls for theoretical tools to analyze such systems.
In the first half, after briefly reviewing recent experimental developments, I will introduce nonperturbative analyses of cavity QED systems based on the asymptotically decoupling unitary transformation [1,2]. In the last half, I will present recent theoretical proposals for controlling moiré materials with a cavity made of van der Waals materials [3].
[1] KM, H. Sudo, M. Oshikawa, and Y. Ashida, PRL 129, 087001 (2022).
[2] KM and Y. Ashida, PRB 107, 195104 (2023)
[3] KM and Y. Ashida, arXiv:2302.11582.
2023年11月10日（金）10:30~（第6回）(6th: 10:30-, Nov. 10, 2023)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Kohei Kawabata (ISSP, Univ. of Tokyo)
Title: Lieb-Schultz-Mattis Theorem in Open Quantum Systems
Abstract:
The Lieb-Schultz-Mattis (LSM) theorem provides a general constraint on quantum many-body systems and plays a significant role in the Haldane gap phenomena and topological phases of matter. Here, we extend the LSM theorem to open quantum systems and establish a general theorem that restricts the steady state and spectral gap of Liouvillians based solely on symmetry. Specifically, we demonstrate that the unique gapped steady state is prohibited when translation invariance and U (1) symmetry are simultaneously present for noninteger filling numbers. As an illustrative example, we find that no dissipative gap is open in the spin-1/2 dissipative Heisenberg model while a dissipative gap can be open in the spin-1 counterpart---an analog of the Haldane gap phenomena in open quantum systems. Furthermore, we show that the LSM constraint manifests itself in a quantum anomaly of the dissipative form factor of Liouvillians. We also find the LSM constraints due to symmetry intrinsic to open quantum systems, such as Kubo-Martin-Schwinger symmetry.
Reference: K. Kawabata, R. Sohal, and S. Ryu, arXiv:2305.16496.
2023年10月27日（金）10:30~（第5回）(5th: 10:30-, Oct. 27, 2023)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Yuan Miao (IPMU, Univ. of Tokyo)
Title: Onsager symmetries in Quantum Integrable Models
Abstract:
Quantum integrable models at root of unity values of anisotropy are of vital importance, due to their rich symmetries associated with quantum groups. I will demonstrate the Onsager symmetries of the spin-1/2 XXZ chain at root of unity, the archetypical quantum integrable spin chains. The Onsager symmetry implies not just infinitely many commuting conserved charges, but also infinitely many of them that do not commute with each other. The importance of the (infinitely many) non-commuting charges has not been thoroughly studied in the case of thermodynamics and hydrodynamics of the quantum integrable models. I will briefly mention some possible applications of the (infinitely many) non-commuting charges.
2023年10月20日（金）10:30~（第4回）(4th: 10:30-, Oct. 20, 2023)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Takashi Oka (ISSP, Univ. of Tokyo)
Title: Heterodyne Hall effect in oscillating magnetic fields
Abstract:
Floquet engineering [1] realizes new dynamic functions in quantum materials. Heterodyning is a signal processing technique that generates output signals by mixing the input signal with the dynamics of the multiplier [2]. The multiplier is a Floquet system that is driven periodically in time [2, 3]. One can use electrons in oscillating magnetic fields as the multiplier and realize the Heterodyne Hall effect [2], which is now extended to Dirac electrons [4].
In this talk, after explaining the basics of the heterodyne Hall effect, I want to share my questions regarding the effect. One question is about the effect of interaction. Would we obtain a fractional quantum Hall state as in static magnetic fields? The second question is regarding bulk edge correspondence. Currently, we think that the effect is not related to topology, and bulk-edge correspondence does not exist. However, this may be too naïve.
[1] T. Oka and S. Kitamura, Annu. Rev. Condens. Matter Phys. 10, 387 (2019).
[2] T. Oka, L. Bucciantini, Phys. Rev. B 94, 155133 (2016).
[3] A. Kumer, M. Rodriguez-Vega, T. Pereg-Barnea, B. Seradjeh, Phys. Rev. B 101, 174314 (2020).
[4] S. Kitamura, T. Oka, in preparation.
2023年10月13日（金）10:30~（第3回）(3rd: 10:30-, Oct. 13, 2023)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Yuki Sughiyama (The University of Tokyo)
Title: Geometry of thermodynamic dynamical system for chemical reaction network
Abstract:
Thermodynamics endows us with the framework to find an equilibrium state, which a macroscopic system converges to. The second law guarantees that the system must climb up a concave landscape of the entropy function; as a result, the equilibrium state is given by the top of the landscape, if the entropy function is bounded above. However, for the system which has many complex constraints such as chemical reaction networks (CRNs), the entropy function is often unbounded and the system may not have the equilibrium state. In this case, where is the system relaxing? Also, if the convergence exists, what can we say about the dissipation structure with it? In this talk, we tackle these problems.
In the first half, we review the thermodynamics on CRNs and reveal the condition for the existence of the equilibrium state. Also, if it exists, we characterize the equilibrium state by employing the Hessian structure. In the second half, to analyze the case without the equilibrium state, we define the thermodynamic dynamical system by introducing the generalized Onsager transport theory (De Giorgi structure). Then, we geometrically investigate its fixed points. Finally, we discuss the decomposition of the entropy production by using the fixed points.
[1] Y. Sughiyama, D. Loutchko, A. Kamimura, T. J. Kobayashi, Phys. Rev. Research 4, 033065 (2022)
[2] T. J. Kobayashi, D. Loutchko, A. Kamimura, Y. Sughiyama, Phys. Rev. Research 4, 033208 (2022)
2023年10月6日（金）10:30~（第2回）(2nd: 10:30-, Oct. 6, 2023)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Naomichi Hatano (The University of Tokyo)
Title: How we came up with the Hatano-Nelson model
Abstract: I will describe how we came up with the non-Hermitian extension of the Anderson-localization model, so called the Hatano-Nelson model, in Ref. [1]. David Nelson and I defined the model as an effective one to describe a flux line depinning in high-Tc superconductors. I will explain some details of the derivation including the path-integral mapping [2].
2023年9月21日（木）15:00~（第1回）(1st: 15:00-, Sept. 21, 2023)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Keita Omiya (EPFL, Paul Scherrer Institute )
Title: Non-thermal eigenstates in non-thermal Hamiltonians with fractionalization
Abstract:
Since anomalously long-lasting oscillations were observed in the experiment of strongly interacting Rydberg atoms, non-thermal eigenstates in non-integrable Hamiltonians, usually referred to as quantum many-body scar (QMBS) states, have attracted some attention as they might form a new class of weak ergodicity-breaking. On one hand many toy models hosting scar states have a common structure: Hamiltonian is a sum of a simple Zeeman term and local projectors, each of which annihilates the scar states. On the other hand, this structure has not been thought to be universal, apparently failing to cover, for example, the scar states in the Affleck-Kennedy-Lieb-Tasaki (AKLT) model and the effective model of the Rydberg experiment known as the PXP model. In this seminar I will first introduce some of the basic notions of the QMBS with a particular emphasis on this common feature and then discuss how the AKLT and the PXP model can indeed fit into this formalism. If time permits, I will also briefly address a simple no-go argument which prohibits “non-trivial” structures in Hamiltonian under certain conditions.
2023年6月30日（金）10:30~（第7回）(7th: 10:30-, June 30, 2023)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Dr. Ryusuke Hamazaki
Title: Universality, breakdown, and timescale of thermalization in isolated quantum systems
Abstract:
How isolated quantum systems relax to thermal equilibrium is the fundamental problem in quantum statistical mechanics [1]. While local observables in generic systems are believed to thermalize after long time via the eigenstate thermalization hypothesis (ETH) [2], to what extent the ETH universally holds is still an open question; indeed, recent studies show that thermalization breaks down by various mechanisms. Furthermore, understanding timescale for thermalization is another challenge beyond the theory of the ETH.
In this talk, we address universality, breakdown, and timescale of thermalization in isolated quantum systems. We first show our numerical verification of the universality of the ETH for realistic quantum many-body systems. We introduce few-body random matrix ensembles to model realistic systems and show that the ETH holds for most of them unless the range of the interactions is too long [3].
We then discuss some new mechanisms that break the ETH in non-integrable systems. We start with high-dimensional quantum Ising models with a weak transverse field. Despite its non-integrability, we discover that the domain-wall conservation law in the effective model leads to the Hilbert-space fragmentation, a recently found mechanism for the absence of thermalization [4]. We next show how general discrete symmetries should break the ETH for a certain class of non-local observables, especially emphasizing the case where higher-form symmetries exist [5].
If time allows, we discuss quantum speed limits useful for the macroscopic transitions, such as macroscopic transport of atoms, which are relevant for timescales of thermalization from inhomogeneous initial states. Employing the local conservation law of probability, we derive quantum speed limits that lead to reasonable timescales for macroscopic transitions [6].
[1] J. Eisert, M. Friesdorf, and C. Gogolin, Nat. Phys. 11, 124 (2015).
[2] M. Rigol, V. Dunjko, M. Olshanii, Nature 452, 854 (2008)
[3] S. Sugimoto, R. Hamazaki, and M. Ueda, Phys. Rev. Lett. 126 (12), 120602 (2021); Phys. Rev. Lett. 129 (3), 030602 (2022).
[4] A. Yoshinaga, H. Hakoshima, T. Imoto, Y. Matsuzaki, and R. Hamazaki, Phys. Rev. Lett. 129 (9), 090602 (2022).
[5] O. Fukushima and R. Hamazaki, arXiv:2305.04984 (2023).
[6] R. Hamazaki, PRX Quantum 3 (2), 020319 (2022).
2023年6月23日（金）10:30~（第6回）(6th: 10:30-, June 23, 2023)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Mr. Atsushi Iwaki (The University of Tokyo)
Title: Random sampling for thermal quantum states
Abstract:
A given quantum state in a thermal equilibrium always has a facultativity in the way how they are described at the microscopic level. The two limiting cases are the Gibbs state which is the exponentially large number of mixtures of pure states with zero purity, and the thermal pure quantum (TPQ) state which is a single quantum state with purity-1. Here, we propose a series of thermal mixed quantum (TMQ) states that have purity between 0 and 1 [1]. We regard all of them as describing the same thermal equilibrium in the sense that they are indistinguishable if we focus on the local observables or the density matrix of a relatively large but small enough subsystem. In this work, we develop an analytical formulation to describe the purity of the TMQ state generated by random samplings. We apply this formula to the TPQ-MPS method [2] and the RPMPS+T method [3], demonstrating that the purity can be measured and can explain the features of these methods. In addition, we will introduce recent analytical results on the sample complexity of the TPQ-MPS method.
[1] A. Iwaki and C. Hotta, PRB 106, 094409 (2022).
[2] A. Iwaki, A. Shimizu, and C. Hotta, PRResearch 3, L022015 (2021).
[3] S. Goto, R. Kaneko, and I. Danshita, PRB 104, 045133 (2021).
2023年6月16日（金）10:30~（第5回）(5th: 10:30-, June 16, 2023)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Dr. Keiichi Tamai (Institute for Physics of Intelligence, The University of Tokyo)
Title: Universal Scaling Laws of Absorbing Phase Transitions in Complex Systems
Abstract:
The notion of universality in critical phenomena, which is well-known for equilibrium phase transitions, can be extended to non-equilibrium ones [1,2]. While non-equilibrium critical phenomena were primarily of theoretical interest in the last century, recent progress suggests that they may be relevant for a deeper understanding of practically important complex systems. In this talk, I will focus on absorbing phase transitions (transitions to a state from which systems cannot escape) to see this point in more detail. After a brief recap on the scaling theory for non-equilibrium critical phenomena, I will demonstrate how universal scaling laws can be seen in various complex systems; in particular, open shear flows in the transitional regime [3,4] and classical artificial deep neural networks near the edge of chaos [5].
[1] H. Hinrichsen. Adv. Phys. 49, 815 (2000).
[2] M. Henkel, H. Hinrichsen, S. Lübeck. Non-equilibrium Phase Transitions. Vol. 1 (Springer, 2008).
[3] M. Sano & KT. Nat. Phys. 12, 249 (2016).
[4] K. Kohyama, M. Sano, KT & T. Tsukahara. Proceedings of TSFP-12 (2022).
[5] KT, T. Okubo, T. V. T. Duy, N. Natori & S. Todo. Under review.
2023年6月9日（金）10:30~（第4回）(4th: 10:30-, June 9, 2023)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Mr. Kouhei Fukai（ISSP）
Title: Factorization of correlation function in the Temperley-Lieb models
Abstract:
Calculating correlation functions in quantum many-body systems poses a significant challenge, even in integrable systems. Several quantum integrable systems, including the spin-1/2 XXZ chain, critical Potts model, and golden chain, can be represented by the Temperley-Lieb algebra.
In this talk, I will present a factorization formula for short-range correlation functions for operators constructed from the Temperley-Lieb generators, which appears to hold true in all representations of the Temperley-Lieb algebra [1]. The correlation function is computed using an energy eigenstate, and the factorization formula works for all eigenstates. The factorization is based on the generalized current operators which satisfy the continuity equation[2], and the correlation function is expressed as the sum of the product of the expectation value of the generalized current operators. Furthermore, I will present a method for constructing the generalized current operators from the local conserved quantities.
[1] K. Fukai, B. Pozsgay, and E. Vernier, arXiv in preparation
[2] M. Borsi, B. Pozsgay, and L. Pristyák, Phys. Rev. X, 2020
2023年6月2日（金）10:30~（第3回）(3rd: 10:30-, June 2, 2023)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Dr. Shohei Imai (The University of Tokyo)
Title: Theory of attosecond dynamics of electrons in solids driven by optical electric fields
Abstract:
Ultrafast science has been expanding its frontiers to the attosecond world. Since excited states are not yet relaxed or disturbed by the environment or electron-electron interactions on this time scale, many unprecedented phenomena arising from quantum coherent dynamics are expected. One of the fundamental phenomena in attosecond physics is high harmonic generation, which has been observed in various crystalline solids and has recently been used to uncover electronic structures such as dispersion relations, electric dipole moments, and topological properties [1]. However, the generation of attosecond pulses, which are important for time-resolved spectroscopy, has been limited in terms of the coherent dynamics of electrons in solids.In this study, we investigate the real-time quasiparticle dynamics induced by a few-cycle pulse with a strong electric field. We show that the emission from the optically driven quasiparticles is described by the wave packet dynamics of the particles. In the case of resonantly excited electrons, the emission turns out to be an echo of the excitation pulse when the quasiparticle wave packets recombine [2]. Furthermore, introducing an ansatz of tunneling electron--hole pairs, we show that attosecond pulses approaching the Fourier limit can be generated through optimized optical driving of tunneling particles in solids [3].
[1] S. Imai, A. Ono, and S. Ishihara, Phys. Rev. Lett. 124, 157404 (2020).
[2] S. Imai, A. Ono, and S. Ishihara, Phys. Rev. Research 4, 043155 (2022).
[3] S. Imai, A. Ono, arXiv:2303.13169.
2023年5月26日（金）10:30~（第2回）(2nd: 10:30-, May 26, 2023)
理学部1号館206教室 (Room No. 206, Science 1st Bldg.)
Speaker: Prof. Hosho Katsura (University of Tokyo)
Title: Duality, criticality, topology, and integrability in quantum spin-1 chains (slides)
Abstract:
In quantum spin-1 chains, a non-local unitary transformation known as the Kennedy-Tasaki (KT) transformation defines the duality between a symmetry-protected topological (SPT) phase and a conventional symmetry-breaking phase. In this talk, I will introduce a one-parameter family of models interpolating between the spin-1 bilinear-biquadratic chain and its dual obtained by the KT transformation [1]. Remarkably, the self-dual model, which is invariant under the KT transformation, maps to an integrable spin-1/2 XXZ chain doped by immobile holes, thereby allowing us to locate the critical line and multicritical point exactly. Furthermore, I will show that the topological and trivial Ising critical lines that are dual to each other meet at the multicritical point in the entire phase diagram.
[1] Hong Yang, Linhao Li, Kouichi Okunishi, and Hosho Katsura, Phys. Rev. B 107, 125158 (2023). [arXiv:2203.15791]
2023年3月8日（水）13:00~（第15回）(15th: 13:00-, March 8, 2023)
理学部4号館1220教室 (Room No. 1220, Science 4th Bldg.)
Speaker: Prof. Kareljan Schoutens (University of Amsterdam)
Title: Supersymmetric lattice models
Abstract:
This seminar will introduce supersymmetry as a remarkable and potent symmetry in lattice models in condensed matter. Our original proposal (Fendley, Schoutens, de Boer 2003) specifies a N=2 supersymmetric Hamiltonian on a general graph. This so-called M_1 model, which features hopping terms and local interactions, exhibits remarkable properties. In 1D it turns out to be integrable and critical, and it connects to a supersymmetric version of Conformal Field Theory, first considered in the String Theory literature. On many 2D lattices, the M_1 model shows superfrustration: a proliferation of zero-energy supersymmetric ground states. Generalizations such as M_k models and models with staggered supercharges enrich the supersymmetric landscape. We end the seminar with a proposal for a quantum simulation of the 1D M_1 model using Rydberg atoms.
2022年12月16日（金）14:00~15:00（第14回）(14th: 14:00-15:00, December 16, 2022)
Speaker: Dr. Toshihiro Sato (Universität Würzburg)
Title: A fermionic quantum Monte Carlo approach to frustrated spin systems
Abstract:
Monte Carlo methods are exact: for a given lattice size and temperature, we obtain the correct result. However, many spin and fermion models suffer from the infamous negative sign problem that renders the computational cost exponential in the volume of the system and in the inverse temperature. A key question is hence how to optimize the sign problem in the absence of sign-free formulations. In this talk, we introduce a phase pinning approach in the realm of the auxiliary field quantum Monte Carlo algorithm to mitigate the severity of the sign problem inherent to Monte Carlo methods of frustrated spin models [1]. This allows us to access high-temperature properties of the aforementioned models and, for instance, carry out exact quantum Monte Carlo simulations in a window of temperatures relevant to experiments for various frustrated magnets. As an example, we study a generalized Kitaev model on a honeycomb lattice. The generalized Kitaev model describes a frustrated spin system which, among other spin orders, supports a spin liquid phase [2]. It is also of remarkable interest due to its relation to honeycomb compounds such as the family of layered iridates and a ruthenium chloride. In fact we show that this phase pinning approach has the ability of reproducing experimental data of the material ruthenium chloride for the so-called magnetotropic coefficient that measures the magnetic rigidity [3]. Using this phase pinning approach, we also introduce a negative sign free formulation of the auxiliary field quantum Monte Carlo algorithm for a set of generalized Kitaev models with higher symmetries [4].
[1] T. Sato and F. F. Assaad, Phys. Rev. B. 104, L081106 (2021).
[2] A. Kitaev, Annals of Physics 321, 2 (2006).
[3] K. A. Modic, et al. Nature Physics (2020).
[4] T. Sato and F. F. Assaad, Phys. Rev. B. 106, 155110 (2022).
2022年12月9日（13）10:30~11:30（第13回）(13th: 10:30am-11:30am, December 9, 2022)
Speaker: Dr. Kazuya Fujimoto (Tokyo Institute of Technology)
Title: Growth of particle-number fluctuations in one-dimensional quantum systems
Abstract
Dynamical scaling originally developed in classical surface growth is recently explored in isolated quantum systems. The examples include the Kardar-Parisi-Zhang scaling in the spin-1/2 XXX model [1,2,3] and the Family-Vicsek (FV) scaling in the Hubbard model [4,5]. Against this background, we pose a fundamental question: Does such dynamical scaling emerge even in open quantum dynamics? To answer this question, we theoretically study a one-dimensional open quantum system using a Gorini–Kossakowski–Sudarshan–Lindblad(GKSL) equation with dephasing. Our exact numerical calculation finds the emergence of the FV scaling featuring a diffusive dynamical exponent, which corresponds to the Edwards-Wilkinson model. Furthermore, we can analytically explain such diffusive dynamics by applying a perturbative renormalization-group analysis to the GKSL equation. In this seminar, first introducing our previous work on the FV scaling in isolated quantum systems [4,5], we show the numerical and analytical results of the open quantum system [6].
-Reference-
[1] M. Ljubotina, M. Znidaric, and T. Prosen, Phys. Rev. Lett. 122, 210602 (2019).
[2] M. Dupont, J. E. Moore, Phys. Rev. B 101, 121106 (2020).
[3] D. Wei et al., Science 376, 716 (2022).
[4] K. Fujimoto, R. Hamazaki, and Y. Kawaguchi, Phys. Rev. Lett. 124, 210604 (2020).
[5] K. Fujimoto, R. Hamazaki, and Y. Kawaguchi, Phys. Rev. Lett. 127, 090601 (2021).
[6] K. Fujimoto, R. Hamazaki, and Y. Kawaguchi, Phys. Rev. Lett. 129, 110403 (2022).
2022年12月2日（12）10:30~11:30（第12回）(12th: 10:30am-11:30am, December 2, 2022)
Speaker: Dr. Yoshiyuki Matsuki (Osaka University)
Title: Fractal defect states in the Hofstadter butterfly
Abstract
The Hofstadter butterfly is a fractal energy spectrum of Bloch electrons in a periodic lattice under a magnetic field, and it is one of the first quantum fractals discovered in physics. After about 40 years since the theoretical prediction, the Hofstadter butterfly was experimentally realized in 2D moiré superlattices and so on. Currently, however, the experimental observation is limited to the measurement of the energy spectrum and the transport properties. Actually, richer fractal information is encoded in the Bloch wavefunctions themselves, but it has not been clarified yet. We investigate the electronic properties of the Bloch electron on a two-dimensional lattice with a point defect under the uniform magnetic field, and establish a theoretical formalism on the rich spatial fractal information of the Hofstadter butterfly. Our results provide a new quantitative perspective on the fractal nature, and a powerful way to elucidate the fractality of the Hofstadter butterfly.
2022年11月25日（11）10:30~11:30（第11回）(11th: 10:30am-11:30am, November 25, 2022)
Speaker : Dr. Mayuko Yamashita (Kyoto University)
Date : Friday, 25 November 2022, 10:30 ~ 11:30 JST
Title : Cobordism picture for QFTs and algebraic topology
Abstract :
There are many mathematical ways to formulate physical systems, such as Hamiltonian picture and Lagrangian picture. Cobordism picture is one of them.
Intuitively, it is given by allowing spacetime to have nontrivial topology. This formulation leads to interesting relations with geometry and topology.
In this talk, I motivate and explain the cobordism picture, and explain the role of algebraic topology in their classification.
2022年11月11日（10）10:30~11:30（第10回）(10th: 10:30am-11:30am, November 11, 2022)
Speaker : Dr. Takashi Imamura (Chiba University)
Date : Friday, 11 November 2022, 10:30 ~ 11:30 JST
Title : KPZ models and free fermions at finite temperature
Abstract :
The Kardar-Parisi-Zhang (KPZ) universality class is a typical
universality class in nonequilibrium statistical mechanics, which characterizes universal properties of fluctuations in various probabilistic
models including surface growth processes, directed polymer models, interacting particle processes etc. In one-dimensional case, there are quite a few exactly solvable models having nice mathematical structures, through which we can access not merely scaling exponents but exact limiting distributions of some observables.
In particular by using techniques in combinatorics and (quantum) integrable system such as the Robinson-Schensted-Knuth (RSK) correspondence, Macdonald symmetric polynomials, Bethe ansatz (and usually after quite complicated calculations), we find the limiting distributions or their Laplace-like transforms can be expressed as Fredholm determinants. It has been a longstanding problem to understand the origin of such determinantal structures.
In this talk, I will introduce a connection between the KPZ solvable models and free fermions at finite temperature, which clarifies the origin of the determinant structure. This connection is summarized as an identity between marginals of two probability measures related to symmetric polynomials, the q-Whittaker measures and the periodic Schur measures. The former describes the KPZ models while the later does the free fermions. We obtain this identity by introducing a new combinatorial approach called the skew RSK dynamics. This is a joint work with Matteo Mucciconi and Tomohiro Sasamoto
(arXiv:2106.11922).
2022年11月4日（9）10:30~11:30（第9回）(9th: 10:30am-11:30am, November 4, 2022)
Speaker : Dr. Toshiya Hikihara (Gunma University)
Date : Friday, 04 November 2022, 10:30 ~ 11:30 JST
Title : Optimization of the network strcuture in tree-tensor-network approaches
Abstract :
Tensor networks (TNs) have attracted increasing interest in various fields including condensed-matter physics, quantum information, data science, quantum cosmology, and so on. In the context of quantum many-body physics, TNs have been employed in several theoretical approaches as TNs has proven to be powerful for representing low-energy states of quantum systems accurately. The ability of TNs to represent quantum states generally depends on their network structure. However, finding the optimal structure for a target state is a nontrivial problem, especially when the system treated is complex, and in the practical application of TN methods, the network structure is usually selected rather intuitively. It is desired to establish a scheme which can routinely find the optimal network structure.
In this talk, I focus on the tree-tensor network (TTN), which is a TN without loops, and introduce two numerical approaches to search for the optimal structure of TTN. The first one is the tensor-network strong-disorder renormalization group method[1-4] for quantum systems with randomness. In the method, the TTN is constructed from the bottom to the top of the network referring to the energy spectrum of spin-block Hamiltonians or the entanglement between spin blocks. The second approach is the numerical variational method with the structural optimization algorithm[5]. During the sweep procedure over the TTN, the network structure is improved by local reconnection of the network using the entanglement distribution in the target state as an evaluation function. I explain the basic ideas and algorithms of the methods and discuss their performance in practical calculations of various quantum spin systems.
[1] T.Hikihara, A.Furusaki, M.Sigrist, Phys.Rev.B 60, 12116 (1999)
[2] A.M.Goldsborough, R.A.Romer, Phys.Rev.B 89, 214203 (2014)
[3] K.Seki, T.Hikihara, K.Okunishi, Phys.Rev.B 102, 144439 (2020)
[4] K.Seki, T.Hikihara, K.Okunishi, Phys.Rev.B 104, 134405 (2021)
[5] T.Hikihara, H.Ueda, K.Okunishi, K.Harada, T.Nishino, arXiv:2209.03196
2022年10月28日（8）10:30~11:30（第8回）(8th: 10:30am-11:30am, October 28, 2022)
Speaker: Tomio Petrosky (The University of Texas at Austin, IIS, The University of Tokyo)
Title: Optical Vortex emitted by Classical Radiation Dumping due to Classical Van Hove singularity near Cut-off frequency in a Waveguide
Abstract
Classical radiation dumping has been a controversial subject because of an acausal solution of the Lorentz-Abraham (LA) equation that involves the third derivative in time. This is in contrast with the quantum mechanics where the second quantization formulation on the radiation process due to the quantum transition of a charged particle has been exactly solved without any contradiction to the fundamental laws of physics in the well-known Friedrichs-Lee model. We have shown that the classical radiation dumping is also analyzed without any contradiction to the fundamental laws by classicizing the commutation relation of the annihilation and destruction operators to the Poisson bracket of the normal modes of the classical field [1]. In this talk we apply this classical formulation to the emission process of an optical vortex with an angular momentum from a cyclotron motion of an electron in a cylindrical waveguide. The optical vortex from a cyclotron radiation has been already experimentally observed [2]. We will show an interesting mechanism of emission of the optical vortex dew to the Van Hove singularity of the density of state of the classical electro-magnetic field appearing at the cut-off frequencies of the waveguide. This new mechanism of emission process cannot be described in terms of the LA equation, because one cannot use the perturbation analysis performed in the LA equation, due to the Van Hove singularity. Our formulation is based on the complex spectral analysis of the Liouvilian that is closely related to the eigenvalue problem of the non-Hermitian operators.
[1] T. Petrosky, G. Ordonez and I. Prigogine, Phys. Rev. A 68 (2003) 022107.
2022年10月21日（金）10:30~11:30（第8回）(8th: 10:30am-11:30am, Oct. 21, 2022)
Speaker: Dr. Tokiro Numasawa (ISSP, Univ. of Tokyo)
Title: SYK Lindbladian
Abstract:
We study the Lindbladian dynamics of the Sachdev-Ye-Kitaev (SYK) model, where the SYK model is coupled to Markovian reservoirs with jump operators that are either linear or quadratic in the Majorana fermion operators.
Here, the linear jump operators are non-random while the quadratic jump operators are sampled from a Gaussian distribution. In the limit of large N, where N is the number of Majorana fermion operators, and also in the limit of large N and M, where M is the number of jump operators, the SYK Lindbladians are analytically tractable, and we obtain their stationary Green’s functions, from which we can read off the decay rate.
For finite N, we also study the distribution of the eigenvalues of the SYK Lindbladians.
Then, we consider the time evolution of the dissipative form factor, which quantifies the average overlap between the initial and time-evolved density matrices as an open quantum generalization of the Loschmidt echo.
We find that the dissipative form factor exhibits dynamical quantum phase transitions.
We analytically demonstrate a discontinuous dynamical phase transition in the limit of large number of fermion flavors, which is formally akin to the thermal phase transition in the two-coupled SYK model between the black-hole and wormhole phases.
We also find continuous dynamical phase transitions that do not have counterparts in the two-coupled SYK model.
Furthermore, we numerically show that signatures of the dynamical quantum phase transitions remain to appear even in the finite number of fermion flavors.
2022年6月27日（月）10:30~11:30（第7回）(7th: 10:30am-11:30am, June 27, 2022)
Speaker: Nathanan Tantivasadakarn (Harvard University)
Title: Pivot Hamiltonians: a tale of symmetry, entanglement, and quantum criticality
Abstract
I will introduce the notion of Pivot Hamiltonians, a special class of Hamiltonians that can be used to "generate" both entanglement and symmetry. On the entanglement side, pivot Hamiltonians can be used to generate unitary operators that prepare symmetry-protected topological (SPT) phases by "rotating" the trivial phase into the SPT phase. This process can be iterated: the SPT can itself be used as a pivot to generate more SPTs, giving a rich web of dualities. Furthermore, a full rotation can have a trivial action in the bulk, but pump lower dimensional SPTs to the boundary, allowing the practical application of scalably preparing cluster states as SPT phases for measurement-based quantum computation. On the symmetry side, pivot Hamiltonians can naturally generate U(1) symmetries at the transition between the aforementioned trivial and SPT phases. The sign-problem free nature of the construction gives a systematic approach to realize quantum critical points between SPT phases in higher dimensions that can be numerically studied. As an example, I will discuss a quantum Monte Carlo study of a 2D lattice model where we find evidence of a direct transition consistent with a deconfined quantum critical point with emergent SO(5) symmetry.
This talk is based on arXiv:2107.04019, 2110.07599, 2110.09512
2022年6月20日（月）10:30~11:30（第6回）(6th: 10:30am-11:30am, June 20, 2022)
Speaker: Dr. Kazuaki Takasan (Univ. of Tokyo)
Title: Activity-induced quantum phase transitions: A proposal for quantum active matter
Abstract:
Active matter is a collection of elements that move by themselves, such as a flock of birds or fish. It has been gathering great attention because it shows phase transitions and pattern formations prohibited in equilibrium [1]. The physics of active matter has been investigated mainly in classical systems. In particular, the application to biophysics has been successful and helps to understand the nature of biological systems [2]. On the other hand, the applications to quantum systems are very limited. It is reasonable because active matter needs nonequilibrium open many-body systems that have not been realized in experiments until recently. However, advances in atomic-molecular-optical experiments now allow us to access such systems and observe the quantum phase transitions induced by dissipation [3]. Thus, it is now sensible to consider the quantum versions of active matter physics.
Based on this background, we recently proposed a quantum many-body model that can be regarded as a quantum analog of active matter, and showed that it exhibits various activity-induced quantum phase transitions [4]. The model consists of two-component hard-core bosons on a lattice with non-Hermitian hopping that resembles activity in classical systems. We studied this model with exact diagonalization and quantum Monte Carlo simulation, and then obtained its phase diagram including various nonequilibrium phases, such as a flocking phase. Also, we have proposed an experimental setup to realize this model using ultracold atoms in optical lattices.
In this seminar, I would like to talk about this work [4], starting from my basic motivation about nonequilibrium phases of matter (This talk has an aspect of the self-introduction because I newly joined to UTokyo in April 2022). If time allows, I will talk about a recent ongoing project about quantum active matter [5].
[1] M. C. Marchetti et al., Rev. Mod. Phys. 85, 1143 (2013).
[2] K. Kawaguchi et al., Nature 545, 327 (2017).
[3] T. Tomita et al., Sci. Adv. 3, e1701513 (2017).
[4] K. Adachi, KT, K. Kawaguchi, Phys. Rev. Research 4, 013194 (2022).
[5] KT, K. Kawaguchi, K. Adachi, in preparation.
2022年6月13日（月）10:30~11:30（第5回）(5th: 10:30am-11:30am, June 13, 2022)
Speaker: Dr. Takanobu Taira (IIS, The University of Tokyo)
Title: Time-dependent PT-symmetric Quantum Mechanics
Abstract:
In 1998, Carl Bender and Stefan Boettcher numerically showed that some non-Hermitian Hamiltonian has a real and bounded energy spectrum [1]. This result has motivated many researchers to develop well-defined quantum mechanics for the non-Hermitian Hamiltonian in a closed system. However, the main problem was the non-positive definiteness of the Dirac inner product. This issue was resolved by the introduction of the C-operator [2].
In this talk, I will briefly introduce the PT-symmetric Quantum Mechanics using the concept of quasi-Hermiticity, combined with pseudo-Hermiticity (both of which will be defined in this talk). Our recent work on the time-dependent non-Hermitian Hamiltonian is also reported [3], where we have found the relation between the C operator and the Lewis-Riesenfeld invariant.
If the time permits, I will also list some applications of PT-symmetric quantum mechanics in different physics and mathematics, such as the Higgs mechanism, Solitons and Skyrmions.
[1]. Bender, Carl M., and Stefan Boettcher. "Real spectra in non-Hermitian Hamiltonians having P T symmetry." Physical review letters 80.24 (1998): 5243.
[2]. Bender, Carl M., Dorje C. Brody, and Hugh F. Jones. "Complex extension of quantum mechanics." Physical Review Letters 89.27 (2002): 270401.
[3]. Fring, Andreas, Takanobu Taira, and Rebecca Tenney. "Time-dependent C-operators as Lewis-Riesenfeld invariants in non-Hermitian theories." arXiv preprint arXiv:2202.10965 (2022).
2022年6月6日（月）10:30~11:30（第4回）(4th: 10:30am-11:30am, June 6, 2022)
Speaker: Dr. Sosuke Ito (Universal Biology Institute, University of Tokyo)
Title: Optimal transport theory as a geometric theory of non-equilibrium thermodynamics
Abstract:
The optimal transport theory known as the Monge-Kantrovich transportation problem is a branch of mathematical theory related to differential geometry, information theory, and stochastic process [1], widely used in economics, machine learning, biological data processing, and physics. For example, in physics, especially in stochastic thermodynamics, the measure of the optimal transport theory called the L_2-Wasserstein distance provides the fundamental limit of the minimum entropy production in a finite time for the overdamped Fokker-Planck equation [2]. Based on this fact, we recently discussed the geometric aspects of the entropy production for the overdamped Fokker-Planck equation. We derived several thermodynamic trade-off relations, such as thermodynamic speed limit and thermodynamic uncertainty relations, and showed the geometric protocol for the optimal heat engine in a finite time and the geometric decomposition of the entropy production into housekeeping and excess parts in the steady-state thermodynamics [3,4,5]. In this seminar, I would like to give an elementary lecture on the mathematical aspect of the optimal transport theory and briefly introduce our recent results.
[1] C. Villani, Optimal transport: old and new. (Berlin: springer, 2009).
[2] E. Aurell, C. Mejía-Monasterio, & P. Muratore-Ginanneschi, Optimal protocols and optimal transport in stochastic thermodynamics. Physical review letters, 106 (2011).
[3] M. Nakazato & S. Ito, Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance. Physical Review Research, 3, 043093 (2021).
[4] A. Dechant, S. I. Sasa & S. Ito, Geometric decomposition of entropy production in out-of-equilibrium systems. Physical Review Research, 4, L012034 (2022).
[5] A. Dechant, S. I. Sasa & S. Ito, Geometric decomposition of entropy production into excess, housekeeping and coupling parts. arXiv:2202.04331 (2022).
2022年5月30日（月）10:30~11:30（第3回）(3rd: 10:30am-11:30am, May 30, 2022)
Speaker: Dr. Makiko Sasada (The University of Tokyo )
Title: Topological structures and the role of symmetry in the hydrodynamic limit of nongradient models
Abstract:
Recently, we introduce a general framework in order to systematically investigate hydrodynamics limits of various microscopic stochastic large scale interacting systems in a unified fashion. In particular, we introduced a new cohomology theory called the uniformly cohomology to investigate the underlying topological structure of the interacting system. Our theory gives a new interpretation of the macroscopic parameters, the role played by the group action on the microscopic system, and the origin of the diffusion matrix associated to the macroscopic hydrodynamic equation. Furthermore, we rigorously formulate and prove for a relatively general class of models Varadhan’s decomposition of closed forms, which plays a key role in the proof of hydrodynamic limits of nongradient models. Our result is applicable for many important models including generalized exclusion processes, multi-species exclusion processes, exclusion processes on crystal lattices and so on. Based on joint papers with Kenichi Bannai and Yukio Kametani.
References:
[1] K.Bannai, Y. Kametani, and M. Sasada, “Topological Structures of Large Scale Interacting Systems via Uniform Functions and Forms” (https://arxiv.org/abs/2009.04699)
[2] K. Bannai and M. Sasada, “Varadhan's Decomposition of Shift-Invariant Closed L2-forms for Large Scale Interacting Systems on the Euclidean Lattice” (https://arxiv.org/abs/2111.08934)
2022年5月23日（月）10:30~11:30（第2回）(2nd: 10:30am-11:30am, May 23, 2022)
Speaker: Niclas Heinsdorf (Max Planck Institute for Solid State Research)
Title: Topological Phase in the Excitation Spectrum of a Quantum Paramagnet
Abstract
Similar to the classification of topological features in electronic band structures, degeneracies in the excitation spectrum of magnets can be assigned topological invariants as well. However, in most cases the features of interest lie high in energy such that these states cannot be thermally populated, since the magnetic order would melt before sufficient temperatures are reached. Because magnetic order breaks the continuous spin-rotational symmetry, Goldstone modes, which extent all the way down to zero energy, offer many available scattering channels to states that are higher in energy, conceivably destroying a topological phase. Here, we investigate the excitation spectrum of a quasi one-dimensional quantum paramagnet that is gapped and more robust in the presence of thermal fluctuations or higher-order magnon-magnon interactions, and show that by applying an external magnetic field a topological phase transition can be enforced.
2021年12月6日（月）13:00~14:00（第15回）(15th: 1pm-2pm, Dec 6, 2021)
Speaker: Dr. Takashi Mori (RIKEN)
Title: Stochastic differential equation approach to machine learning dynamics
Abstract
In recent unparalleled success of deep learning, stochastic gradient descent (SGD) or its variants plays a crucial role as an efficient training algorithm. Although the loss landscape is highly nonconvex, the SGD often succeeds in finding a global minimum. It has been argued that the SGD noise plays a key role in escaping from local minima. It has also been suggested that SGD has an implicit bias that is beneficial for generalization. That is, SGD may help the network to find flat minima, which are considered to imply good generalization. How and why does SGD help the network escape from bad local minima and find flat minima? These questions have been addressed in several works, and it is now recognized that the SGD noise strength and structure importantly affect the efficiency of escape from local minima.
In this talk, I explain our recent work [1] following this line of research. We derived a stochastic differential equation (SDE) as a continuous-time approximation of SGD, and investigated the property of SGD noise. It turns out that SGD noise strength significantly depends on the position in the parameter space, and is proportional to the loss function that should be minimized. By using this property, we introduced a random time change that transforms the original SDE with complicated multiplicative noise into a simple SDE with additive noise. I discuss the Kramers escape problem by using this simplified SDE.
2021年11月29日（月）13:00~14:00（第14回）(14th: 1pm-2pm, Nov. 19, 2021)
Speaker: Dr. Sota Kitamura (U. Tokyo)
Title: Nonreciprocal current response in the Landau-Zener problem
Abstract:
One of the growing interests in recent studies of nonlinear responses
is nonreciprocal phenomena where transport toward the left and the
right differs. Typically, nonreciprocal transport requires the
breaking of both time-reversal and spatial-inversion symmetries, which
leads to an asymmetric energy dispersion. The emergence of
nonreciprocity in the presence of the time-reversal symmetry is thus a
nontrivial issue.
In this talk, we show that noncentrosymmetric insulators can exhibit
nonreciprocity in the tunneling phenomena, due to the geometric phase
effect [1,2]. In noncentrosymmetric systems, electron-hole pairs can
have a finite polarization. This is quantified by the shift vector,
which corresponds to the difference of the Berry connection between
the two states on the valence and conduction bands. By taking account
of the geometric effect explicitly, we show that the Landau-Zener
formula for the tunneling probability has a direction-dependent
geometric correction expressed by the shift vector, and the resultant
nonperturbative current response acquires nonreciprocity.
[1] S. Kitamura, N. Nagaosa, and T. Morimoto, Commun. Phys. 3, 63 (2020).
[2] S. Kitamura, N. Nagaosa, and T. Morimoto, Phys. Rev. B 102, 245141 (2020).
2021年11月22日（月）13:00~14:00（第13回）(13th: 1pm-2pm, Nov. 22, 2021)
Speaker: Dr. Naoto Shiraishi (Gakushuin University)
Title: Undecidability in quantum thermalization
Abstract:
A quantum many-body system at a nonequilibrium initial state will relax to the unique equilibrium state, which is called thermalization. Almost all physical quantum many-body systems are considered to show thermalization. On the other hand, some quantum many-body systems including integrable systems do not thermalize. One of the central problems in quantum thermalization is to find the conditions determining whether thermalization occurs in a given system. Despite vast literature in this field, this problem has still been left as an open problem.
We tackle this problem with a completely different approach from previous ones. Applying the viewpoint of theoretical computer science, we clarify the hardness of the problem of quantum thermalization. Surprisingly, we find that this problem is undecidable [1]. Our result is still valid even when the system is one-dimensional, Hamiltonian is shift-invariant and nearest-neighbor interaction, the initial state is a product state, and the observable is a shift-sum of a one-body observable.
References:
[1] N. Shiraishi and K. Matsumoto, Nat. Comm. 12, 5084 (2021)
2021年11月15日（月）13:00~14:00（第12回）(12th: 1pm-2pm, Nov. 15, 2021)
Speaker: Prof. Tomotoshi Nishino (Kobe University)
Title: Effects of energy scale deformations on discrete lattice Hamiltonians
Abstract:
We consider effects of a slow spacial variation on interaction parameter introduced to lattice Hamiltonians. A typical example is the 1-dimensional antiferromagnetic Heisenberg spin chain, where the strength of the neighboring interaction varies sinusoidally. Under this sine square deformation (SSD), the ground state is totally uniform, although the Hamiltonian is not translationally invariant. This phenomenon can be explained by the fact that the uniform part of the Hamiltonian H_0 and the slowly modulated part H_I have a common eigenstate, which is nothing but the ground state. We then have a question: Does this mathematical structure exist also in higher dimension? Let us check this point for the Heisenberg model on polyhedral lattices. Numerical data shows that the ground state is highly insensitive to the interaction modulation. We discuss other type of deformations if time allows.
arXiv:0810.0622, 1012.0472, 1012.1472, 2109.10565
http://quattro.phys.sci.kobe-u.ac.jp/SSD/SSD.html
2021年11月8日（月）13:00~14:00（第11回）(11th: 1pm-2pm, Nov. 8, 2021)
Speaker: Dr. Tokuro Shimokawa (OIST)
Title: Unbiased numerical study of the quantum spin liquid material Ca10Cr7O28
Abstract:
Ca10Cr7O28 is a new and novel quantum spin liquid material [1-4]. Despite the complexity of the proposed spin Hamiltonian [1] (a bilayer-breathing kagome structure constructed by five Heisenberg-type interactions, including predominant ferromagnetic ones), specific heat, susceptibility, μSR, and INS measurements didn't exhibit any magnetic order nor spin-glass freezing down to 19mK.
In the first half of this talk, we will explore the origin of the quantum spin-liquid behavior in Ca10Cr7O28 by using nonbiased numerical methods such as a recently developed high-field exact diagonalization code [5]. We find that the proposed spin-1/2 bilayer-breathing kagome Heisenberg model can exhibit several quantum spin liquid behaviors observed in experiments [6]. These quantum data can also support a semiclassical scenario of a spiral spin liquid state in Ca10Cr7O28 [4].
Secondly, we will also explore the possible realization of several multiple-q states in Ca10Cr7O28. It was reported that a J1-J2 classical honeycomb-lattice model could be a good effective model for this material [2,4]. We investigate the low-temperature physics of the honeycomb-lattice system using large-scale Monte Carlo simulations and succeed in finding a sub-lattice skyrmion/anti-skyrmion lattice state with a topological nature [7].
References
[1] C. Balz, et al, Nat. Phys. 12, 942 (2016).
[2] S. Biswas and K. Damle, Phys. Rev. B 97, 115102 (2018).
[3] J. Sonnenschein et al, Phys. Rev. B 100, 174428 (2019).
[4] R. Pohle, H. Yan, and N. Shannon, Phys. Rev. B 104, 024426 (2021).
[5] H. Ueda, S. Yunoki and T. S. arXiv:2107.00872.
[6] T. S., R. Pohle, and N. Shannon, in preparation.
[7] T. S. and R. Pohle, in preparation.
2021年11月1日（月）13:00~14:00（第10回）(10th: 1pm-2pm, Nov. 1, 2021)
Speaker: Dr. Hideaki Obuse (Hokkaido Univ.)
Title: Non-Hermitian physics and non-unitary quantum walks
Abstract:
Recently, non-Hermitian physic which is related to open quantum systems has attracted great attention from the various fields of physics, i.e., condensed matter physics, classical and quantum optics, cold atoms, etc. While there are many experiments to imitate non-Hermitian Hamiltonians in classical systems, it is not easy to experimentally realize a true quantum system related to non-Hermitian Hamiltonians in a controlled way. At the moment, a discrete-time quantum walk (quantum walk, in short) by using entangled photons is one of the most ideal platforms to realize the non-Hermitian quantum system and study the novel phenomena in experiment.
In this talk, we introduce a non-unitary quantum walk to realize the non-Hermitian quantum system and explain various non-Hermitian phenomena by combining theoretical and experimental results. First, we explain the novel non-Hermitian topological phases for real gaps in the non-unitary quantum walks, i.e., the observation of topological edge states[1,2,3] and a breakdown of the bulk-edge correspondence[4]. Then, we explain the skin effect originating from the non-Hermitian topological phase for point gaps in the quantum walk[5]. Furthermore, we will also talk about that the localization-delocalization transition in the non-Hermitian one dimensional disordered system, which has been studied by a well known Hatano-Nelson tight-binding model so far, can be realized by using the non-unitary quantum walk[6].
[1] K. Mochizuki, D. Kim, and H. Obuse, Phys. Rev. A 93, 062116 (2016).
[2] K. Mochizuki, D. Kim, N. Kawakami, and H. Obuse, Phys. Rev. A 102, 062202 (2020).
[3] L. Xiao, X. Zhan, Z.H. Bian, et al, Nature Phys. 13, 1117 (2017).
[4] M. Kawasaki, K. Mochizuki, N. Kawakami, and H. Obuse, Prog. Theor. Exp. Phys. 2020, 12A105 (2020).
[5] R. Okamoto, N. Kawakami, and H. Obuse (in preparation).
[6] N. Hatano and H. Obuse, Annals of Physics (accepted, arXiv:2107.10420).
2021年10月18日（月）13:00〜14:00（第9回）(9th: 1pm-2pm, Oct. 18, 2021)
Speaker: Dr. Yusuke Nomura (RIKEN CEMS)
Title: Quantum many-body problems and artificial neural networks
Abstract:
It is a great challenge to accurately represent quantum many-body states. In this talk, we will show that Boltzmann machines used in machine learning can be useful for analyzing quantum many-body systems.
First, we introduce a method for representing quantum states using Boltzmann machines proposed by Carleo and Troyer in 2017 [1]. Then, we discuss the progress of the neural-network wave function method for zero-temperature simulations [2-6]. Through various extensions, the neural-network wave functions are beginning to be applied to challenging problems (e.g., frustrated spin systems) in physics [5].
Next, we discuss two finite-temperature calculation methods using deep Boltzmann machines (DBMs) with two hidden layers [7]. Both methods use the idea of “purification,” where a finite-temperature mixed state is represented by a pure state of an extended system. The former analytically constructs a pure state corresponding to thermal equilibrium, realizing quantum-to-classical mapping [3]. The latter method obtains the pure state by numerically optimizing the DBM parameters. This method can be applied to, e.g., frustrated systems for which the former method suffers from the negative sign problem. We will discuss the applications to the transverse-field Ising model and J1-J2 Heisenberg model.
These works were done in collaboration with Andrew S. Darmawan, Youhei Yamaji, Masatoshi Imada, Giuseppe Carleo, Nobuyuki Yoshioka, and Franco Nori.
[1] G. Carleo and M. Troyer Science 355, 602 (2017)
[2] Y. Nomura, A. S. Darmawan, Y. Yamaji, and M. Imada, Phys. Rev. B 96, 205152 (2017)
[3] G. Carleo, Y. Nomura, and M. Imada, Nat. Commun. 9, 5322 (2018)
[4] Y. Nomura, J. Phys. Soc. Jpn. 89, 054706 (2020) [Editor’s choice]
[5] Y. Nomura and M. Imada, Phys. Rev. X 11, 031034 (2021)
[6] Y. Nomura, J. Phys.: Condens. Matter 33, 174003 (2021) [special issue “Emergent Leaders 2020"]
[7] Y. Nomura, N. Yoshioka, and F. Nori, Phys. Rev. Lett. 127, 060601 (2021)
2021年10月11日（月）13:00〜14:00（第8回）(8th: 1pm-2pm, Oct. 11, 2021)
Speaker: Dr. Satoru Hayami (University of Tokyo)
Title: Engineering nonreciprocal magnon excitations based on magnetic toroidal moment
Abstract:
Noncentrosymmetric magnets have drawn considerable interest in condensed matter physics, since they show various fascinating phenomena, such as the magneto-electric effect and the nonreciprocal transport. One of the features in noncentrosymmetric magnets is to exhibit an asymmetric magnon band structure with respect to the wave number [1], which is referred to as nonreciprocal magnons. Recently, such nonreciprocal magnons have been observed in noncentrosymmetric magnets, but its microscopic understanding has not been fully achieved.
In the present study, we introduce a concept of magnetic toroidal (MT) moment, which is a fundamental moment appearing in the absence of both spatial inversion and time-reversal symmetries [2]. We show that the MT moment can be used as not only a symmetry descriptor but also microscopic quantity to characterize the nonreciprocal magnons. We discuss the results in several antiferromagnets including the zigzag chain, honeycomb, and breathing kagome structures. We present the symmetry and model parameter conditions of emergent nonreciprocal magnons [3-6]. We also propose an efficient method to extract the essential model parameters without the Bogoliubov transformation [6].
[1] R. L. Melcher, Phys. Rev. Lett. 30, 125 (1973).
[2] N. A. Spaldin, M. Fiebig, and M. Mostovoy, J. Phys.: Condensed Matter 20, 434203 (2008).
[3] S. Hayami, H. Kusunose, and Y. Motome, J. Phys. Soc. Jpn. 85, 053705 (2016).
[4] T. Matsumoto and S. Hayami, Phys. Rev. B 101, 224419 (2020).
[5] T. Matsumoto and S. Hayami, arXiv:2107.12743 (2021).
[6] S. Hayami and T. Matsumoto, submitted.
2021年7月5日（月）10:00〜11:00（第7回）(7th: 10am-11am, July 5, 2021)
Speaker: Prof. Hosho Katsura (University of Tokyo)
Title: Experimental mathematical physics
Abstract:
In this talk, I will discuss how to discover nontrivial exact results for many-body systems using cutting-edge technologies on the internet like the On-Line Encyclopedia of Integer Sequences (OEIS) [1] and Inverse Symbolic Calculator (ISC) [2]. I will first review some classic examples where "guesswork" based on extensive numerical calculations was successful. Then, I will talk about some supernatural experiences that I had while exploring quantum many-body systems [3, 4]. If time allows, I will also discuss some open problems that seem to be within reach of the current technology.
[2] http://wayback.cecm.sfu.ca/projects/ISC/ISCmain.html
[3] E. Iyoda, H. Katsura, and T. Sagawa, Phys. Rev. D 98, 086020 (2018).
[4] N. Sannomiya, H. Katsura, and Y. Nakayama, Phys. Rev. D 95, 065001 (2017).
2021年6月28日（月）10:00〜11:00（第6回）(6th: 10am-11am, Jun. 28, 2021)
Speaker: Dr. Yuta Murakami (Tokyo Tech)
Title: Nonthermal orders in strongly correlated systems
Abstract:
One of the major goals in nonequilibrium condensed matter physics is to control or induce ordered phases by exciting matters.
In particular, strongly correlated systems is an attracting playground to this direction.
In this talk, we discuss two ideas about how to realize nonthermal orders in strongly correlated systems.
The first idea is to use the prethermal regime before the scatterings set in [1].
In this regime, the information of the initial state is kept so that the system can remain cold in a certain sense even after the excitation.
We demonstrate that this concept can be used to induce a nonthermal excictonic order in a multi-orbital Hubbard model.
The second idea is to use a possible bottleneck in the relaxation process in Mott insulators.
By exciting Mott insulators, one induces pseudoparticles that are absent in equilibrium.
These pseudoparticles may have long lifetime due to a large Mott gap (bottleneck), which leads the system to approach a nonequilibrium steady state.
By introducing a generalized Gibbs ensemble type description for strongly correlated systems, we studied the photo-doped one-dimensional extended Hubbard model [2].
We determined the nonequilibrium phase digram of this model, where the eta-pairing phase, spin density wave and charge density wave compete or coexist.
We reveal the properties of these nonequilibrium phases and clarify unique features compared to chemically doped states in equilibrium.
We also discuss the relation between these nonthermal orders in strongly correlated systems and those in photo-excited semiconductors, which have been discussed for decades.
[1] P. Werner and Y. Murakami, Phys. Rev. B 102 241103(R) (2020).
[2] Y. Murakami, S. Takayoshi, T. Kaneko, Z. Sun, D. Golež, A. J. Millis and P. Werner, arXiv:2105.13560.
2021年6月21日（月）10:00〜11:00（第5回）(5th: 10am-11am, Jun. 21, 2021)
Speaker: Prof. Gen Kimura (Shibaura Institute of Technology)
Title: Universal constraint on relaxation times for Quantum Dynamical Semigroup
Abstract: In order to realize practical quantum devices such as quantum computer, one always has to overcome a noise, especially a decoherence, in order to keep a quantum coherence. However, the general nature of decoherence is still missing even from the theoretical point of view. Quantum dynamical semigroup describes a general Markovian dynamics of an open quantum system, incorporating the conditions of complete positivity (CP) and trace preservation (TP). The generator of the equation has a nice representation which is nowadays called a GKLS (Gorini-Kossakowski-Lindblad-Sudarshan) generator. A decoherence process is characterized by relaxation times, from which one knows a time scale to keep a quantum coherence. In this talk, we discuss there is a universal constraint for relaxation times which is satisfied for any GKLS generator, i.e., for any quantum dynamical semigroup. By introducing new matrix inequalities, which themselves are interesting from mathematical point of view, we derive several constraints tighter than the bounds known so far. We also give a conjecture for the tightest constraint. Due to the universality and its experimental accessibility, we believe that our constraint gives a physical manifestation of the completely positive condition (in the same spirit of Bell's theorem).
References:
* V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, J. Math. Phys. 17, 821 (1976).
* G. Lindblad, Commun. Math. Phys. 48, 119 (1976).
* G. Kimura, Phys. Rev. A 66, 062113 (2002).
* G. Kimura, S. Ajisaka, K. Watanabe, Open Syst. Inform. Dynam. 24(4): 1-8 (2017).
* D. Chruscinski, G. Kimura, A. Kossakowski, Y. Shishido, arXiv:2011.10159 (2020).
* G. Kimura, R. Fujii, H. Hiromichi, D. Chruscinski (in prep.)
2021年6月14日（月）10:00〜11:00（第4回）(4th: 10am-11am, Jun. 14, 2021)14
Dr. Sergio Andraus (U. Tokyo)
Title: Fractal dimension of collision times in a log-potential Brownian particle system
Abstract:
Starting in the 1960s, the study of one-dimensional Brownian particle systems conditioned never to collide has been an important research topic due to its relationship to multiple polymer chains in two dimensions [1], and wetting and melting transitions [2] among many others. The non-colliding constraint manifests itself as a logarithmic repulsion potential between particles with a couplingconstant beta equal to two. These systems, more generally known as the Dyson model [3], can be defined for any real positive value of beta, but the non-colliding property disappears when beta lies between zero and one [4], suggesting the existence of some sort of phase transition. While it is known that in this "high temperature regime" particles collide almost surely, the properties of the collision times have been unclear until now. We focus on the set of collision times, and we find that it has a fractal structure. Moreover, we show that the fractal dimension of the set is non-zero when beta lies between zero and one, and that it vanishes when beta is greater than one, which is a behavior that resembles that of an order parameter.
This is joint work with N. Hufnagel, TU Dortmund.
[1] P. G. de Gennes, J. Chem. Phys. 48 (1968) 2257 - 2259
[2] M. E. Fisher, J. Stat. Phys. 34 (1984) 667 - 729
[3] F. J. Dyson, J. Math. Phys. 3 (1962) 1191 - 1198
[4] N. Demni, C. R. Acad. Sci. Paris, Ser. I 347 (2009) 1125 - 1128
2021年6月7日（月）10:00〜11:00（第3回）(3rd: 10am-11am, Jun. 7, 2021)
秋山 進一郎氏（筑波大）Mr. Shinichiro Akiyama (Univ. of Tsukuba)
Title: Tensor renormalization group approach to fermions on a lattice
Abstract:
Tensor renormalization group (TRG) approach is a variant of the real-space renormalization group to evaluate the path integral in the thermodynamic limit, without resorting to any probabilistic interpretation for the given Boltzmann weight. Moreover, since the TRG can directly deal with the Grassmann variables, this approach can be formulated in the same manner for the systems with bosons, fermions, or both of them. These advantages of the TRG approach have been confirmed by the earlier studies of various lattice theories, which suggest that that the TRG potentially enables us to investigate the parameter regimes where it is difficult to access with the standard stochastic numerical methods, such as the Monte Carlo simulation.
In this talk, we explain our recent applications of the TRG approach to fermions on a lattice. Investigating both relativistic and non-relativistic interacting lattice fermions based on the path-integral formalism, we discuss the efficiency of the TRG approach, especially in the higher dimensions.
2021年5月31日（月）10:00〜11:00（第2回）(2nd: 10am-11am, May 31, 2021)
原田健自氏（京大）Dr. Kenji Harada (Kyoto Univ.)
Title: Universal spectrum structure on the nonequilibrium critical line of the one-dimensional Domany-Kinzel cellular automaton
Abstract:
The Domany-Kinzel(DK) cellular automaton is a stochastic time-evolutional system with an absorbing state from which the system cannot escape and a canonical model for nonequilibrium critical phenomena[1]. We introduce the tensor network method as a new tool to study it. Estimating the entropy of the DK automaton with a matrix product state representation of distribution, we reported a new cusp of the Renyi entropy in the active phase of the DK cellular automaton[2]. We recently applied a tensor renormalization group method to transfer matrices at the nonequilibrium critical point of the DK cellular automaton, confirming a universal spectrum structure[3]. In this talk, we will report our results with a brief review of models and methods.
[1] M. Henkel, H. Hinrichsen, and S. Lübeck, Non-Equilibrium Phase Transitions. Volume 1: Absorbing Phase Transitions, Vol. 1 (Springer, 2008).
[2] K. H. and N. Kawashima, Entropy Governed by the Absorbing State of Directed Percolation, Physical Review Letters 123, 090601 (2019).
[3] K. H., Universal spectrum structure at nonequilibrium critical points in the (1+1)-dimensional directed percolation, arXiv:2008.10807.
2020年11月25日（水）10時から Wednesday, November 11, 2020, 10am
松崎雄一郎氏（産総研）Dr. Yuichiro Matsuzaki (AIST)
Title: Quantum annealing with long-lived qubits
Abstract
Quantum annealing (QA) provides us with a way to solve specific problems such as finding a ground state of Ising Hamiltonians or estimating an energy of quantum chemistry Hamiltonians. In the previous demonstrations of the QA, superconducting flux qubits (FQs) was used. However, the flux qubits in these demonstrations have a short coherence time such as a few nanoseconds, and so it was not clear whether quantum properties were exploited. Here, we describe a novel QA scheme to use capacitively shunted flux qubits (CSFQs) having a few order of magnitude better coherence time than the FQ. We theoretically show that, although it is difficult to perform the conventional QA with the CSFQ due to the form and strength of the interaction between the CSFQs, a spin-lock based QA can be implemented with the CSFQ even with the current technology. Moreover, we show an example of how long-lived qubits such as CSFQs can be utilized to solve practically useful problems.
2020年11月18日（水）10時から Wednesday, November 18, 2020, 10am
古賀昌久氏（東工大） Dr. Akihisa Koga (Tokyo Inst. Tech.)
Title: Magnetic and transport properties in the generalized Kitaev model
Abstract:
The Kitaev model [1] have attracted much interest in condensed matter physics since the possibility of direction-dependent Ising interactions has been proposed in realistic materials [2]. One of the important features characteristic of the Kitaev models is the fractionalization of the spin degree of freedom. In the Kitaev model with S = 1/2 spins, the spins are exactly shown to be fractionalized into itinerant Majorana fermions and localized fluxes. Two energy scales for distinct degrees of freedom yield interesting finite temperature properties, such as a double-peak structure in the specific heat and plateau in the entropy [3]. This fractionalization is closely related to the existence of the local Z2 symmetry in the system.
The existence of the local Z2 symmetry is known even in the generalized spin-S Kitaev model [4], while it is still unclear whether or not the spin fractionalization occurs in the system. To clarify this, in this study, we examine thermodynamic properties in the generalized Kitaev model. We then clarify the existence of the double-peak structure in the specific heat and plateau in the entropy [5], which suggests the existence of fractionalization even in this spin-S Kitaev model.
We also discuss transport properties in the Kitaev model, examining the real-time and real-space dynamics of the system with zigzag edges. After the magnetic-field pulse is introduced to one of the edges, spin moments are excited in the opposite edge region although spin moments are never induced in the Kitaev quantum spin liquid region. This unusual spin transport originates from the fact that the S=1/2 spins are fractionalized into the itinerant and localized Majorana fermions. Although both Majorana fermions are excited by the magnetic pulse, only the itinerant ones flow through the bulk regime without spin excitations, resulting in the spin transport in the Kitaev system [6]. Transport properties in the S=1 Kitaev system are also addressed [7].
[1] A. Kitaev, Ann. Phys. 321, 2 (2006).
[2] G. Jackeli and G. Khaliullin, Phys. Rev. Lett. 102, 017205 (2009).
[3] J. Nasu, M. Udagawa, and Y. Motome, Phys. Rev. B 92, 115122 (2015).
[4] G. Baskaran, D. Sen, and R. Shankar, Phys. Rev. B 78, 115116 (2008).
[5] A. Koga, H. Tomishige, and J. Nasu, J. Phys. Soc. Jpn. 87, 063703 (2018).
[6] T. Minakawa et al., Phys. Rev. Lett. 125, 047204 (2020).
[7] A. Koga et al., J. Phys. Soc. Jpn. 89, 033701 (2020).
2020年11月11日（水）10時から Wednesday, November 11, 2020, 10am
桑原知剛氏（理研）Dr. Tomotaka Kuwahara (RIKEN)
Title: Improved thermal area law and quasi-linear time algorithm for quantum Gibbs states
Abstract:
One of the most fundamental problems in quantum many-body physics is the characterization of correlations among thermal states. Of particular relevance is the thermal area law which justifies the tensor network approximations to thermal states with a bond dimension growing polynomially with the system size. In the regime of sufficiently low temperatures which is crucially important for practical applications the existing techniques do not yield optimal bounds. Here we propose a new thermal area law that holds for generic many-body systems on lattices. We improve the temperature dependence from the original O(\beta) to \tilde{O}(\beta^{2/3}) thereby suggesting diffusive propagation of entanglement by imaginary time evolution. This qualitatively differs from the real-time evolution which usually induces linear growth of entanglement. We also prove analogous bounds for the Rényi entanglement of purification and the entanglement of formation. Our analysis is based on a polynomial approximation to the exponential function which provides a relationship between the imaginary-time evolution and random walks. Moreover for one-dimensional (1D) systems with n spins we prove that the Gibbs state is well-approximated by a matrix product operator with a sublinear bond dimension. This allows us to rigorously establish for the first time a quasi-linear time classical algorithm for constructing an MPS representation of 1D quantum Gibbs states at arbitrary temperatures of = o(log(n)). Our new technical ingredient is a block decomposition of the Gibbs state that bears resemblance to the decomposition of real-time evolution given by Haah et al. FOCS’18.
This is a joint work with Alvaro Alhambra (Max Planck institute) and Anurag Anshu (UC Berkley).
Reference: T. Kuwahara, A. M. Alhambra and A. Anshu, arXiv:2007.11174
2020年11月4日（水）10時から Wednesday, November 4, 2020, 10am
赤城 裕氏（東京大学） Dr. Yutaka Akagi (U. Tokyo)
Title: Noncommutative indices for disordered topological phases
Topological phases of matter have recently attracted considerable attention due to their nontrivial gapless edge/surface states robust against perturbations. They exhibit various fascinating phenomena such as topological magnetoelectric effects in three-dimensional topological insulators [1] and the realization of Majorana fermions [2]. In translationally invariant systems, topological invariants that characterize the topological phases are defined in terms of Bloch wave functions. However, it is not obvious how to define such an invariant in disordered systems, where crystal momentum is no longer a good quantum number.
Recently, it was found that the methods of noncommutative geometry [3] provide a mathematically rigorous way to define topological invariants (noncommutative indices) for non-interacting fermions [4], which is particularly useful for studying systems without translational symmetry. In practice, however, it is nontrivial to obtain the indices from finite-size calculations since they are defined in the infinite-volume limit. To overcome this, we have developed a numerical method to compute the noncommutative indices [5]. We here take the Wilson-Dirac-type Hamiltonian in class AII as an example and demonstrate how the noncommutative formula allows us to map out the phase diagram even in the presence of disorder. Our results are consistent with those obtained by a transfer-matrix method in previous work [6].
We also generalized the noncommutative indices to bosonic Bogoliubov-de Gennes systems, which possess a unique mathematical property – non-Hermiticity [7-9]. These indices are defined in terms of the projector onto the states below a fictitious Fermi energy. To demonstrate the validity of the definition, we study an artificial spin ice model that describes disordered magnon Hall systems in two dimensions [10]. In the clean limit, the topological index perfectly coincides with the conventional Chern number. We also show that the topological index is robust against disorder, and the index characterizes the disordered topological and trivial localized magnon phases as we map out the phase diagram [11]. In this presentation, we will discuss how to define the noncommutative indices in detail, and then see how it works in disordered systems.
[1] X. L. Qi, T. L. Hughes, and S. C. Zhang, Phys. Rev. B 78, 195424 (2008).
[2] Y. Kasahara, T. Ohnishi, Y. Mizukami, O. Tanaka, Sixiao Ma, K. Sugii, N. Kurita, H. Tanaka, J. Nasu, Y. Motome, T. Shibauchi, and Y. Matsuda, Nature 559, 227 (2018).
[3] J. E. Avron, R. Seiler, and B. Simon, J. Func. Anal. 120, 220 (1994).
[4] H. Katsura and T. Koma, J. Math. Phys. 59, 031903 (2018).
[5] Y. Akagi, H. Katsura, and T. Koma, J. Phys. Soc. Jpn. 86, 123710 (2017).
[6] K. Kobayashi, T. Ohtsuki, and K. Imura, Phys. Rev. Lett. 110, 236803 (2013).
[7] S. Lieu, Phys. Rev. B 98, 115135 (2018).
[8] K. Kawabata, K. Shiozaki, M. Ueda, and M. Sato, Phys. Rev. X 9, 041015 (2019).
[9] H. Kondo, Y. Akagi, and H. Katsura, Preprint arXiv: 2006.10391 (2020). [Accepted for publication in Progress of Theoretical and Experimental Physics]
[10] B. Xu, T. Ohtsuki, and R. Shindou, Phys. Rev. B 94, 220403(R) (2016).
[11] Y. Akagi, Preprint arXiv: 2010.07762 (2020).
2020年10月28日（水）10時から Wednesday, October 28, 2020, 10am
大橋 遼氏 (東京大学) Mr. Haruka Ohashi (U. Tokyo)
Title: Factorization conjecture in TASEP and zero-range process
Abstract: In this talk, I will introduce that, when observing the steady distribution of cyclic TASEP and TASEP with open boundary conditions, most of the cells are seem to behave independently from the state of the surrounding cells if the system size is sufficiently large. In addition, I'll show that a model called zero-range process, which is very similar to cyclic TASEP, also has a similar property that reflects the characteristics of zero-range process.
2020年10月21日（水）10時から Wednesday, October 21, 2020, 10am
辻 直人氏（理研） Dr. Naoto Tsuji (RIKEN)
Title: Quantum interference fluctuation theorem
Abstract: Fluctuation theorems (FTs) have played a central role in our understanding of how macroscopic irreversibility arises from microscopically reversible dynamics, leading to a number of fundamental relations including the second law of thermodynamics, fluctuation-dissipation relations, and Onsager’s reciprocity relations. For isolated quantum systems, the conventional approach to FTs is based on a two-point projective energy measurement for work, in which the information on off-diagonal elements of the density matrix (i.e., quantum coherence) are thrown away at each measurement. A question that naturally arises is: how does coherence fluctuate after work is done, and what is the relation between work and coherence?
Coherence lies at the heart of quantum mechanics, and has many applications in quantum optics, quantum information, and condensed matter physics. Experimentally, coherence can be probed by the Hong-Ou-Mandel (HOM) interference as indistinguishability of quantum states. In this talk, we study HOM interference between identical systems in which work is performed independently. We show that the distribution of the visibility of HOM interference as a function of the total work satisfies a rigorous relation (quantum interference FT) between forward and backward processes. This provides a nontrivial constraint between work and coherence. We discuss various consequences of the quantum interference FT, including the derivation of the out-of-time-ordered fluctuation-dissipation theorem [1] that relates information scrambling and certain nonlinear response functions. We also discuss that the distribution of the HOM interference visibility is related to non-integrability of quantum many-body systems.
[1] N. Tsuji, T. Shitara, and M. Ueda, Phys. Rev. E 97, 012101 (2018).
2020年10月14日（水）10時から Wednesday, October 14, 2020, 10am
井村健一郎氏（広島大学） Dr. Ken'ichiro Imura (Hiroshima U.)
Title: Non-Hermitian scattering problems and resonances
Abstract: In non-Hermitian scattering problems the behavior of the transmission probability T(k) is very different from its Hermitian counterpart. Even in the case of a single isolated onsite scatterer, it not only exceeds unity, but can be divergent. A pair of divergent peaks collide at an exceptional point and merge into a broad peak. Here, in a Fabry-Perot type PT symmetric model [1], its behavior is shown to be even more spectacular. In the regime of weak non-Hermiticity the behavior of T(k) is strongly non-Hermitian with divergent peaks, while in the regime of strong non-Hermiticity T(k) becomes superficially Hermitian recovering the conventional Hermitian Fabry-Perot type peak structure. The unitarity of the S-matrix is, on the other hand, shown to be generally broken in both of the regimes, but recovered in the limit of infinitely strong non-Hermiticity.
[1] K. Shobe, K. Kuramoto, K.-I. Imura, N. Hatano, “Non-Hermitian Fabry-Perot Resonances in a PT symmetric system,” to appear on arXiv.
2020年10月7日（水）10時から Wednesday, October 7, 2020, 10am （オンライン）
道下佳寛 氏（京都大学） Mr. Yoshihiro Michishita (Kyoto U.)
Title & Abstract: Equivalence of the effective non-Hermitian Hamiltonian in open quantum system and strongly-correlated electron system
Abstract: The phenomena described by the non-Hermitian Hamiltonian have been intensively studied, especially in the context of artificial quantum systems. Effective non-Hermitian Hamiltonian induces novel topological phases [1,2], unusual critical phenomena [3], enhanced sensitivity [4], and so on.
In the open quantum systems (OQS), such as cold atomic systems, it is possible to derive an effective non-Hermitian Hamiltonian under certain conditions even though the Hamiltonian describing the total system is Hermitian. However, as the system becomes large, it becomes difficult to experimentally realize these conditions, such as postselection or a PT-symmetric setup. Thus, experiments about non-Hermitian phenomena in artificial quantum systems are particularly done in one-dimensional or small systems.
On the other hand, in strongly-correlated electron systems (SCES), it is also possible to derive the effective non-Hermitian Hamiltonian describing the spectral function [5]. In this case, the non-hermiticity comes from the scattering by interaction and specific setup, such as postselection or PT-symmetric setup, is not necessary. Thus, it seems easier to observe the bulk 2D or 3D non-Hermitian phenomena in SCES than in OQS. The non-Hermitian physics in SCES also holds the potential to explain the pseudo-gap in curate superconductors or quantum oscillation [6] in the topological Kondo insulator SmB6 and YbB12. Therefore, the non-Hermitian physics in SCES was also studied.
One problem is that the way to introduce the effective non-Hermitian Hamiltonian in each context is quite different, and it is not clear their relation, especially whether they are the same or not.
We close this gap and demonstrate that the non-Hermitian Hamiltonians emerging in both fields are identical, and we clarify the reason why postselection is not necessary to derive a non-Hermitian Hamiltonian in strongly correlated materials [8]. Using this knowledge, we propose a method to analyze non-Hermitian properties without the necessity of postselection by studying specific response functions of open quantum systems and strongly-correlated systems. We have also shown that non-markovness of the dynamics of the single particles in strongly-correlated electron systems is relevant.
In this seminar, I will shortly explain the derivation of the effective non-Hermitian Hamiltonian in SCES and OQS, and talk about our recent work written above [7,8]. If I have good research progress this week, I will also talk a bit about my recent study.
[1] H. Shen, B. Zhen, and L. Fu, Phys. Rev. Lett. 120, 146402 (2018)
[2] Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Phys. Rev. X 8, 031079 (2018)
[3] Y. Ashida, S. Furukawa, and M. Ueda, Nat. Commun. 8, 15791 (2017)
[4] W. Chen, S. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, Nature 548, 192 (2017)
[5] V. Kozii and L. Fu, arXiv:1708.05841 (2017)
[6] H. Shen and L. Fu, Phys. Rev. Lett. 121, 026403 (2018)
[7] Y. Michishita, T. Yoshida, and R. Peters Phys. Rev. B 101, 085122 (2020)
[8] Y. Michishita and R. Peters, Phys. Rev. Lett. 124, 196401(2020)
2020年9月30日10:00〜11:00 (第9回) (9th: 10am-11am, September 30, 2020)（オンライン）
野村清英 氏（九州大学） Dr. Kiyohide Nomura (Kyushu U.)
Title : Multicritical point, conformal field theory and duality
Abstract : Critical phenomena are one of the important subjects in condensed matter physics. Many developments about critical phenomena, such as renormalization group, numerical methods etc. have been done. But, when the model has a multicritical point, the scaling behaviors become difficult due to the interference of multiple critical lines. So, conventional numerical methods are not useful near a multicritical point.
We have studied several multicritical phenomena combining with the conformal field theory and numerical methods (level spectroscopy etc.) [1,2]. And we discuss the relation with the duality, such as the Kramers-Wannier duality and the Ashkin-Teller self-duality [2].
[1] A.Kitazawa and K.N.: Phys. Rev. B 59, 11358
[2] S. Moriya and K. N: J. Phys. Soc. Jpn. 89, 093001 (2020)
2020年7月13日10:00〜11:00 (第8回) (8th: 10am-11am, July 13, 2020)
Title: Session by students for master theses
(Sorry, not open to the public.)
2020年7月6日10:00〜11:15 (第8回) (8th: 10am-11:15am, July 6, 2020)
Title: Session by students for Ph.D. theses
(Sorry, not open to the public.)
2020年6月29日10:00〜11:00 (第7回) (7th: 10am-11am, Jun 29, 2020)
樺島 祥介 氏 (東大理) Yoshiyuki Kabashima (The University of Tokyo)
Title: On replica-BP correspondence in rotation-invariant spin glass models
Abstract:
The replica and cavity methods are two major analytical tools in statistical mechanics of disordered systems. In early 2000s, we showed that the following correspondences between the two methos hold for the Sherrington-Kirkpatrick model, which is a famous solvable model of spin glasses: (1) The macroscopic dynamics of belief propagation (BP), which serves as an efficient algorithm to solve the cavity (or Thouless-Anderson-Palmer: TAP) equation, is described by the naive iterative substitution of the saddle point equation of the replica method under the replica symmetric (RS) ansatz. (2) The instability condition of BP's fixed point accords with the de Almeida-Thouless condition of the RS solution. (1) and (2) also hold when the coupling matrix is given by the Gram matrix of random matrices composed of entries sampled independently from identical distributions. In this talk, we discuss whether these correspondences are further generalized or not for spin glass models that are characterized by rotation-invariant matrix ensembles.
2020年6月22日10:00〜11:00 (第6回) (6th: 10am-11am, Jun 22, 2020)
池田 達彦 氏 (東大物性研) Tatsuhiko Ikeda (ISSP)
Title: General description for nonequilibrium steady states in periodically driven dissipative quantum systems
Abstract:
The Floquet engineering, or controlling material properties and functionalities by time-periodic drives, is one of the forefronts of quantum physics of light-matter interaction [1], but limited to ideal dissipationless systems. For the Floquet engineering extended to a broader class of materials, it is vital to understand the quantum states emerging in a balance of the periodic drive and energy dissipation. Here we derive the general description for nonequilibrium steady states (NESS) in periodically driven dissipative systems by focusing on the systems under high-frequency drive and time-independent Lindblad-type dissipation [2]. Our formula correctly describes the time-average, fluctuation, and symmetry property of the NESS, and can be evaluated efficiently in numerics. Our results apply to various dissipative quantum systems such as atoms and molecules, mesoscopic systems, and condensed matter.
[1] T. Oka and S. Kitamura, Annu. Rev. Condens. Matter Phys. 10, 387 (2019).
[2] T. N. Ikeda and M. Sato, arXiv:2003.02876.
2020年6月15日10:00〜11:00 (第5回) (5th: 10am-11am, June 15, 2020)
李宰河氏（東大） Dr. Jaeha Lee (U. Tokyo)
Title: A Universal Formulation of Uncertainty Relations
Abstract: The uncertainty principle stands undoubtedly as one of the basic tenets of quantum mechanics, characterizing the indeterministic nature of the microscopic world. Since the seminal exposition by Heisenberg in 1927 [1], the uncertainty principle has found various modes of manifestations of different nature in diverse realms, e.g., quantum indeterminacy, measurement error, observer effect, time-energy, and the more recent information-theoretic trade-off relations. This talk provides an overview of the uncertainty principle by primarily focusing on its three orthodox realms regarding quantum indeterminacy, measurement error, and observer effect. A concise review of their historical development, from the earliest mathematical formulations by Kennard [2], Robertson [3] and Schroedinger [4] to the more contemporary Ozawa's formulation [5, 6], will be given. These distinct realms and formulations are then accounted for within a single unified framework based on a recently proposed universal formulation [7-8], which may point towards a unified picture of the various branches of the uncertainty principle.
[1] W. K. Heisenberg, Z. Phys. 43, 172 (1927).
[2] E. H. Kennard, Z. Phys. 44, 326 (1927).
[3] H. P. Robertson, Phys. Rev. 34, 163 (1929).
[4] E. Schroedinger, Sitz.-Ber. Preuss. Akad. Wiss., Phys.-Math. Kl. 19, 296 (1930).
[5] M. Ozawa, Phys. Rev. A 67, 042105 (2003).
[6] M. Ozawa, Phys. Lett. A 320, 367 (2004).
[7] J. Lee and I. Tsutsui, arXiv:2002.04008 (2020).
[8] J. Lee and I. Tsutsui, arXiv:2004.06099 (2020).
2020年6月8日10:00〜11:00 (第4回) (4th: 10am-11am, June 8, 2020)
Dr. Andrew K. Harter (U. Tokyo)
Title: Analysis of Topological States in a Floquet-driven Non-Hermitian System
Abstract:
Non-Hermitian Hamiltonians offer a good description of many open systems in which gain and loss are present; crucially, in contrast to their Hermtian counterparts, they may have a complex eigenspectrum. Interestingly, non-Hermitian Hamiltonians which possess PT symmetry [1] can be shown to admit an entirely real eigenspectrum within a certain range of their parameters. It has been shown [2] that certain PT-symmetric lattices can admit topologically non-trivial phases; however, this phase only coincides with the PT-symmetry broken phase, and the topological edge states correspond to imaginary eigenvalues. We examine Floquet driving of this system which, for high enough driving frequencies [3], has been shown to stabilize the edge states. By using a simple two-step, pulsed time dependence, we explore the entire range of driving frequencies to highlight new regions of stability, including those which are explicitly below the high-frequency regime.
[1] Bender, C. and Boettcher, S. Phys. Rev. Lett. 80, 5243 (1998)
[2] Rudner, M. S. and Levitov, L. S. Phys. Rev. Lett. 102, 065703 (2009)
[3] C. Yuce, Eur. Phys. J. D 69, 184 (2015)
2020年6月1日10:00〜11:00 (第3回) (3rd: 10am-11am, Jun 1, 2020)
宇田川 将文 氏 (学習院大理) Masafumi Udagawa (Gakushuin Univ.)
Title: Spinon dynamics in Quantum spin ice (slides)
Abstract: Fractionalization is one of the most remarkable phenomena in the systems of nontrivial topological character. Spinon give a typical example of fractional excitation, where special interests are focused on its dynamics. In this talk, we will take up quantum spin ice (QSI) as a model system to host spinons in higher dimensions. We model this system with spin-1/2 quantum XXZ model defined on a pyrochlore lattice, and address its dynamics through the exact diagonalization of small clusters, combined with mapping to a network, which we call state graph [1, 2]. As a result, we found the singular change of dynamical spectral function, due to the coupling to background gauge-field degrees of freedom. We will discuss the consequences of this spectral singularity on inelastic neutron scattering experiments [1]. We also present renewed interpretations to several previous theoretical studies on magnetization process of Kagome antiferromagnets [2].
[1] M. Udagawa and R. Moessner, Phys. Rev. Lett. 122, 117201 (2019).
[2] M. Udagawa and R. Moessner, in preparation.
2020年5月25日10:00〜11:00 (第2回) (2nd: 10am-11am, May 25, 2020)
桂 法称 氏 (東大理) Hosho Katsura (UTokyo)
Title: Integrable dissipative spin chains
Abstract: We study two models of dissipative spin chains that can be mapped to integrable non-Hermitian models. The first model is a quantum compass chain with bulk dephasing. I will show that the Liouvillian of the system can be diagonalized exactly by mapping it to a non-Hermitian Kitaev model on a two-leg ladder. The relaxation time and the autocorrelation function of edge spins exhibit different behavior depending on whether the quantum compass Hamiltonian is in a trivial or a topological phase. The second model is a quantum Ising chain with a particular form of the bulk dissipation. In this case, the Liouvillian turns out to be a non-Hermitian Ashkin-Teller model, which can be further mapped to an XXZ spin chain with purely imaginary anisotropy $\Delta$. In both cases, we obtain exact results for the steady states and the Liouvillian gap (the inverse relaxation time) by exploiting the integrability of the systems.
[1] Naoyuki Shibata and Hosho Katsura, Phys. Rev. B 99, 174303 (2019).
[2] Naoyuki Shibata and Hosho Katsura, Phys. Rev. B 99, 224432 (2019).
[3] slides
2020年5月18日10:00〜11:00 (第1回) (1st: 10am-11am, May 18, 2020)
新M1 (New graduate students)
Title: 自己紹介/研究紹介 (Self introduction)
2019年12月17日 15:00〜16:00 (第22回) (22nd: Dec. 17th, 3:00pm-4:00pm)
理学部1号館447教室 (Room 447, Science 1st Bld.)
郡 宏氏 (東大新領域) (Hiroshi Kori, Department of Complexity Science and Engineering)
Title: Mathematical and experimental approach to dynamical phenomena in biology: jet lag, locomotion, fluctuation, etc.
Abstract: Theoretical approach is essential for understanding complex phenomena in a variety of systems, ranging from biology to engineering. In this talk, I will introduce a few recent studies on biological oscillations, in which simple models were useful not only for understanding but also for predicting interesting dynamics. Topics include circadian rhythms [1], jet lag [2,3], fluctuation [4] and locomotion.
References:
[1] Murayama, Y., Kori, H., Oshima, C., Kondo, T., Iwasaki, H., & Ito, H. (2017). Low temperature nullifies the circadian clock in cyanobacteria through Hopf bifurcation. Proceedings of the National Academy of Sciences, 114(22), 5641-5646.
[2] Yamaguchi, Y., Suzuki, T., Mizoro, Y., Kori, H., Okada, K., Chen, Y., ... & Okamura, H. (2013). Mice genetically deficient in vasopressin V1a and V1b receptors are resistant to jet lag. Science, 342(6154), 85-90.
[3] Kori, H., Yamaguchi, Y., & Okamura, H. (2017). Accelerating recovery from jet lag: prediction from a multi-oscillator model and its experimental confirmation in model animals. Scientific reports, 7, 46702.
[4] H. Kori, Y. Kawamura, N. Masuda: “Structure of Cell Networks Critically Determines Oscillation Regularity”, J. Theoretical Biolog 297, pp. 61 – 72, (2012).
(CANCELED) 2019年12月10日 15:00〜16:00 (第21回) (21st: Dec. 10th, 3:00pm-4:00pm)
理学部1号館447教室 (Room 447, Science 1st Bld.)
李 宰河氏 (東大数理)
2019年12月3日 15:00〜16:00 (第20回) (20th: Dec. 3rd, 3:00pm-4:00pm)
理学部1号館447教室 (Room 447, Science 1st Bld.)
松井 千尋氏 (Prof. Chihiro Matsui)
Title: Non-Hermitian quasilocal charges and non-equilibrium behavior of the XXZ model
Abstract:
Recently, the transfer matrices associated with the complex-spin representations have been obtained for the XXZ model. The important properties of these transfer matrices are spin-flip symmetry breaking. We discuss two representative problems of nonequilibrium physics in the integrable XXZ chain by using the spin-flip asymmetric transfer matrices.
1. The relaxation state
The eigenstate thermalization hypothesis (ETH) has been proposed as the mechanism for isolated quantum systems to thermalize. While the ETH holds for all energy eigenstates in non-integrable systems, not all energy eigenstates obey the ETH in integrable systems. Instead, it is believed that the generalized Gibbs ensemble (GGE), which is the generalization of the Gibbs ensemble including many conserved quantities, describes the relaxation state. We conjecture that functionally-independent conserved quantities are enough to describe the relaxation state of the XXZ chain.
2. Ballistic transport of the spin currents
There is a long history about the discussion whether the spin currents in one-dimensional integrable system remain finite or not at finite temperature. It has been showed that the overlap between the current operator and conserve quantities guarantees the existence of the ballistic channel of currents. We discuss the linear independence of spin-flip asymmetric conserved quantities and how they support the ballistic transport of the spin currents in the XXZ model.
Through the discussion of the above two problems, we give the physical meaning to the spin-flip asymmetric conserved quantities.
2019年12月2日(月) 15:00〜16:00 (第19回) (19th: Dec. 2nd (Mon), 3:00pm-4:00pm)
理学部1号館447教室 (Room 447, Science 1st Bld.)
Liang Qin (ENS, Paris): Application of Event-Chain Monte Carlo in Classic Physics Model
Abstract:
What is the algorithm complexity to simulate N Coulomb charges in a box of size L? Most naive Metropolis Monte Carlo takes O(N^2) operations for a sweep, and O(L^2) sweeps to decorrelate samples. Now with the invention of Event-Chain Monte Carlo we are exploring their lower bounds.Event-Chain Monte Carlo is a novel Monte Carlo framework without detailed balance proposed in 2009, and is applicable to any continuous a priori distribution. Deeply exploiting its stochastic nature, ECMC can circumvent force calculation,total energy computation, and even exact potential derivative required by other long-established methods. Furthermore, its unidirectional system move proofs able to achieve global irreversibility, which helps avoid random-walk nature of traditional MC. My talk will consist of two parts. (1) With the example of first O(NlogN)-per-sweep dipole MC algorithm I will show implemental reason for ECMC to be fast. (2) Our discovery of factor field, a counter-intuitive term that reaches O(L^(1/2)) scaling in correlation time for 1D.
References:
[1] M. F. Faulkner, L. Qin, A. C. Maggs, W. Krauth, All-atom computations with irreversible Markov chains Journal of Chemical Physics 149, 064113 (2018)
[2] Ze Lei, Werner Krauth, and A. C. Maggs, Event-chain Monte Carlo with factor fields Phys. Rev. E 99, 043301 (2019)
2019年11月26日 15:00〜16:00 (第18回) (18th: Nov. 26th, 3:00pm-4:00pm)
理学部1号館447教室 (Room 447, Science 1st Bld.)
飯野 隼平氏 (東大物性研): Boundary Tensor Renormalization Group
Abstract:
Tensor renormalization group (TRG) [1] is a numerical method of contracting tensor networks efficiently, by which one can accurately compute partition functions of statistical systems or Euclidean path integrals of quantum many-body systems, since they can be represented as tensor networks simply. Another remarkable feature of TRG is that the local tensors in the network converges to some fixed point tensors under the coarse graining transformations, which are useful to not only characterize the gapped phases of matters, but also extract the conformal data underlying the lattice systems at criticality [2].
In this talk, we will discuss how to apply TRG methods to open-boundary systems, after a brief review on the ordinary TRG algorithms. We extends the so-called higher-order TRG [3] and tensor network renormalization [4], both of which are improved TRG algorithms, so as to simulate the renormalization of boundaries [5,6]. Our methods make it possible to study physics at the boundary such as surface phase transitions by computing surface physical quantities and boundary conformal field theories underlying the critical lattice systems by extracting boundary conformal spectrum. I will present some numerical results for two-dimensional classical spin models.
References:
[1] M. Levin and C. P. Nave, Phys. Rev. Lett. 99, 120601 (2007).
[2] Z.-C. Gu and X.-G. Wen, Phys. Rev. B 80, 155131 (2009).
[3] Z. Y. Xie et al., Phys. Rev. B 86, 045139 (2012).
[4] G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015).
[5] S. Iino, S. Morita, and N. Kawashima, Phys. Rev. B 100, 35449 (2019).
[6] S. Iino, S. Morita, and N. Kawashima, in preparation.
2019年11月19日 15:00〜16:00 (第17回) (17th: Nov. 19th, 3:00pm-4:00pm)
理学部1号館447教室 (Room 447, Science 1st Bld.)
中村 統太氏 (芝浦工大)
Title: Machine learning as an improved estimator formagnetization curve and spin gap
Abstract:
By applying a machine learning algorithm to data extrapolations and the numerical differentiations, we propose a method to obtain a continuous magnetization curve out of discrete energy data, by which we can estimate a magnetization exponent, $\delta$. It also gives another expression for the spin gap, which converges to the thermodynamic limit differently and mostly faster than the original gap definition. A consistent size extrapolation of both spin gap data improves much its accuracy. We checked the validity for an exactly solvable one-dimensional spin model and applied it to the kagome antiferromagnet. Results of the kagome antiferromagnet obtained by the exact-diagonalization data up to 30 sites were comparable to the DMRG results for the 132 sites. The spin gap in the thermodynamic limit was estimated as very small but finite.
2019年11月12日 15:00〜16:00 (第16回) (16th: Nov. 12th, 3:00pm-4:00pm)
理学部1号館447教室 (Room 447, Science 1st Bld.)
Rico Pohle 氏 (早稲田大) (Dr. Rico Pohle, Waseda University)
Title: Origin of the spin liquid behaviour in Ca10Cr7O28
Abstract:
Ca10Cr7O28, a novel spin-1/2 magnet with a bilayer breathing-kagome lattice structure, has properties which differ from any known spin liquid [1]. However, understanding Ca10Cr7O28 presents a significant challenge, because of its complex frustration mechanism.
In this talk, we explore the origin of the spin-liquid behaviour in Ca10Cr7O28, using large-scale classical Monte Carlo and molecular-dynamics simulations [2]. Starting from the spin-1/2 BBK model, proposed by Balz et al. [1], we establish a finite-temperature phase diagram, and directly compare dynamical and thermodynamical properties to experimental data of Ca10Cr7O28.
To our surprise, we find that excitations encode not one, but two distinct types of spin liquids at different time scales. Fast fluctuations reveal a “coulombic spin liquid”, seen by broad “bow-tie” features in the magnetic scattering function. Those features evolve in applied field into distinct “pinch-points” and "half-moons", as known from the classical kagome Heisenberg antiferromagnet [3, 4]. On the other hand, slow fluctuations reveal a gapless “spiral spin liquid”, which can be seen in form of “rings” in the magnetic scattering function, and understood by a mapping onto an effective spin-3/2 model on the Honeycomb lattice [5].
References:
[1] C. Balz, B. Lake, J. Reuther, H. Luetkens, R. Schonemann, T. Herrmannsdorfer, Y. Singh, A. T. M. Nazmul Islam, E. M. Wheeler, J. A. Rodriguez-Rivera, T. Guidi, G. G. Simeoni, C. Baines, and H. Ryll, Nat. Phys. 12, 942 (2016)
[2] R. Pohle, H. Yan, and N. Shannon, arXiv:1711.03778
[3] M. Taillefumier, J. Robert, C. L. Henley, R. Moessner, and B. Canals, Phys. Rev. B 90, 064419 (2014)
[4] H. Yan, R. Pohle, and N. Shannon, Phys. Rev. B 98, 140402 (2018)
[5] S. Biswas and K. Damle, Phys. Rev. B 97, 115102 (2018)
2019年11月5日 15:00〜16:00 (第15回) (15th: Nov. 5th, 3:00pm-4:00pm)
理学部1号館447教室 (Room 447, Science 1st Bld.)
吉野 元氏 (阪大サイバー) (Prof. Hajime Yoshino, Cybermedia Center, Osaka University)
Title: Free-energy landscape of deep neural networks
Abstract:
Machine learning by deep neural networks (DNN) is successful in numerous applications. However it remains challenging to understand why DNNs actually work so well. Given the enormous parameter space, which is typically orders of magnitude larger than that of the data space, and the flexibility of non-linear functions used in DNNs, it is not very surprising that they can express complex data. What is surprising is that such extreme machines can be put under control overcoming seemingly very serious potential problems of over fitting (poor generalization) and slow learning dynamics. In this talk I discuss a statistical mechanical approach based on a replica method to study the phase space structure of a deep neural network which provides clues to understand why DNNs operate efficiently. I also present results of a set of numerical simulations to examine the theoretical predictions. Our work may also have implications on various complex systems with heterogeneity, including gene regulatory networks and allosteric systems.
[1] Hajime Yoshino, "From complex to simple : hierarchical free-energy landscape renormalized in deep neural networks", arXiv:1910.09918.
2019年10月29日 15:00〜16:00 (第14回) (14th: Oct. 29th, 3:00pm-4:00pm)
理学部1号館447教室 (Room 447, Science 1st Bld.)
今村 卓史氏 (千葉大) (Prof. Takashi Imamura, Chiba University)
Title: q-TASEP, stochastic vertex models and the q-Whittaker measures
Abstract:
The q-totally asymmetric simple exclusion process (q-TASEP) is a typical model of stochastic interacting particle system belonging to the Kardar-Parisi-Zhang (KPZ) universality class. Since the introduction in [1], it has been playing an important role in recent progresses in the integrable probability. One interesting feature is that the q-Laplace transform of the particle position distribution can be represented as a single Fredholm determinant. So far various approaches to get this relation have been developed such as the Macdonald process, stochastic duality/Bethe ansatz, Yang-Baxter equation etc. All of these are based on a common idea of finding nice determinantal expressions of the q-moments.
In this talk, we report a different approach to the q-TASEP without using the q-moments [2]. By using the result by Cauchy, Ramanujan and Frobenius, we clarify determinantal structures of the q-Whittaker measure, a probability measure written as a product of two q-Whittaker functions. From this, we obtain a different type of a Fredholm determinant formula of the q-TASEP. We can also analyze the property of the q-TASEP under the non-equilibrium stationary state where the previous approaches have a difficulty that the q-moments diverge. Furthermore this approach can be applicable to the higher spin stochastic vertex models [3], which are generalized stochastic processes to the q-TASEP. This is a joint work with Tomohiro Sasamoto and Metteo Mucciconi.
References
[1] A. Borodin and I. Corwin, Probability Theory and Related Fields, 158, 225-400, 2014 (arXiv:1111.4408)
[2] T. Imamura and T. Sasamoto, Probability Theory and Related Fields, 174, 647-730, 2019 (arXiv:1701.05991)
[3]T. Imamura, M. Mucciconi, and T. Sasamoto, arXiv: 1901.08381
2019年10月15日 15:00〜16:00 (第13回) (13th: Oct. 15th, 3:00pm-4:00pm)
理学部1号館447教室 (Room 447, Science 1st Bld.)
Speaker: 苅宿 俊風氏 Dr. Toshikaze Kariyado (NIMS)
Title: Band flattening by moire patterns in generic type twisted bilayer systems
Abstract:
Twisted bilayer graphene is now attracting huge attention as a controllable avenue to investigate correlated physics. There, it is believed that flat band plays a central role. Here, we demonstrate band flattening in generic types of twisted bilayers with high symmetry, i.e., bilayers of the five 2D Bravais networks [1]. We first establish a theoretical flamework for symmetry-based constraints on the effective potential governing low-energy physics in twisted bilayers. Then, we numerically demonstrate the band flattening compatible with those constraints. From the generic theory, we can find an interesting possibility of anisotropic band flattening, in which quasi 1D band dispersion is generated from relatively isotropic original band dispersion. Rich physics is expected with the anisotropic band flattening, like emergence of a Kugel-Khomskii type spin-orbital intertwined model in the correlated regime.
[1] T. Kariyado and A. Vishwanath, arXiv:1905.02206.
[CANCELED] 2019年10月2日 15:00〜16:00 (第12回) (12th: Oct. 2nd, 3:00pm-4:00pm)
理学部4号館1320教室 (Room 1320, Science 4th Bld.)
Speaker: Prof. Israel Klich (the University Of Virginia)
Title: Highly entangled spin chains and exact holographic tensor networks
Abstract:
Tensor networks provide a useful class of variational wave functions suitable for numerical studies of ground states of quantum hamiltonian as well as certain classical problems. In spite of an extensive body of work on the subject, so far no examples have been found where tensor networks describe exactly ground states of gapless systems. Here, I will describe recent exact constructions of the ground states of the deformed Motzkin and Fredkin models. These models are spin chains that pose a novel quantum phase transition between low and high entanglement, and, as I will show, their ground state can be written as a new type of tensor network, describing tiling models in which the physical degrees of freedom live on the edge.
2019年9月25日 15:00〜16:00 (第11回) (11th: Sep. 25th, 3:00pm-4:00pm)
理学部4号館1220教室 (Room 1220, Science 4th Bld.)
Speaker: Dr. Manas Kulkarni (ICTS-TIFR, Bangalore)
Title: Kardar Parisi Zhang (KPZ) scaling in non-integrable and integrable classical spin chains
Abstract:
We will present results on equilibrium spatio-temporal correlations in classical non-integrable and integrable spin chains. For the non-integrable case, we consider the classical XXZ model (Lattice Landau Lifshitz model) and show regimes where we find KPZ scaling [1]. We explain it using the framework of nonlinear fluctuating hydrodynamics (NFH). To our surprise, we find that a classical integrable spin chain [2] also has regimes in which it displays KPZ behaviour. Our findings are along the lines of what was recently found in quantum integrable spin chains thereby providing strong evidence for a classical-quantum correspondence.
[1] Avijit Das, Kedar Damle, Abhishek Dhar, David A. Huse, Manas Kulkarni, Christian B. Mendl, Herbert Spohn (arXiv:1901.00024, Journal of Statistical Physics, 2019, accepted)
[2] Avijit Das, Manas Kulkarni, Herbert Spohn, Abhishek Dhar (arXiv:1906.02760, PRE 2019, in press)
2019年7月18日16:30〜17:30 (第10回) (10th: July 18th, 4:30pm-5:30pm)
理学部4号館1320教室 (Room 1320, Science 4th Bld.)
笹本智弘氏 Prof. Tomohiro Sasamoto (Tokyo Tech)
Title: Large deviation of spin current for the 1D XX spin chain with domain wall boundary condition
Abstract:
We consider the XX spin chain on the infinite lattice starting with the domain wall initial condition and study the fluctuations of the integrated current of up-spins at the origin between time 0 and t. We give an explicit formula for the large deviation in terms of elliptic integrals and discuss connections to previous works on average and variance. Our analysis is based on the known determinantal formula for the generating function and a connection between the discrete and continuous Bessel kernels.
Reference:
H. Moriya, R. Nagao, and T. Sasamoto J. Stat. Mech. (2019) 063105(arXiv: 1901.07228)
2019年4月25日15:00〜16:00 (第一回) (1st: 3pm-4pm, April 25, 2019)
理学部4号館1320教室 (Room No. 1320, Science 4th Bldg.)
新M1 (New graduate students)
Title: 自己紹介/研究紹介 (Self introduction)
Abstract: N/A
2018年度の統計力学セミナー: http://spin.phys.s.u-tokyo.ac.jp/seminar/mitseminar.html
次回のセミナー