Abstracts
Chris Bourne (AIMR)
Title:
Wannier bases and topology of aperiodic Schrödinger operators
Abstract:
Given a Schrödinger-type operator with a lattice-periodic potential and spectral gap, a Wannier basis is an orthonormal basis of a spectral subspace built from the lattice translates of a finite set of functions. The Bloch-Floquet transform guarantees the existence of such bases, but their regularity changes dramatically depending on whether the spectral subspace forms a trivial vector bundle over the Brillouin torus (momentum space) or not. In this talk, I will review these results and consider an extension to aperiodic Schrödinger operators using an operator algebraic framework. This is joint work with Bram Mesland (Leiden University).
Yuki Chino (National Chiao Tung University )
Title:
Recurrence vs transience in RWCRE
Abstract:
One-dimensional Random Walk in Cooling Random Environment (RWCRE) is obtained as a patchwork of one-dimensional Random Walk in Random Environment (RWRE) by resampling the environment along a sequence of deterministic times. The RWCRE model can be seen as a model that interpolates between the classical static model and the model with i.i.d. resamplings every unit of time. This model shows a crossover between RWRE and a homogeneous model according to how to resample, called the cooling map. The talk is based on the jointwork with L. Avena, C. da Costa and F. den Hollander.
David Croydon (Kyoto University)
Title:
Generalized hydrodynamic limit for the box-ball System
Abstract:
I will talk about a recent joint work with Makiko Sasada (University of Tokyo) in which we obtain a generalized hydrodynamic limit for the box–ball system of Takahashi and Satsuma. This explains how the densities of solitons of different sizes evolve asymptotically under Euler space-time scaling. To describe the limiting soliton flow, we introduce a continuous state space analogue of the soliton decomposition, namely we relate the densities of solitons of given sizes in space to corresponding densities on a scale of ‘effective distances’, where the dynamics are linear. For smooth initial conditions, we further show that the resulting evolution of the soliton densities in space can alternatively be characterised by a partial differential equation, which naturally links the time-derivatives of the soliton densities and the ‘effective speeds’ of solitons locally.
Yukimi Goto (RIKEN)
Title:
The Maximal Excess Charge in Reduced Hartree-Fock Molecule
Abstract:
In this talk, I will explain the ionization conjecture within the reduced Hartree-Forck theory of molecules. The ionization conjecture is a long-standing open problem in mathematical physics and states that the possible negative ionization is bounded by some constant independent of the total nuclear charge. So far, the ionization conjecture of atoms in reduced Hartree-Fock theory has been proven by Jan Phillip Solovej. The purpose of this talk is to extend Solovej’s result to molecular cases under certain conditions.
Kohei Hayashi (The university of Tokyo)
Title:
Derivation of a stochastic Burgers equation from stationary square lattice polymers
Abstract:
We consider scaling limits of the log-partition function (free energy) for fully discrete (1+1)-dimensional directed polymers with stationarity which are called four basic beta-gamma models. We show that fluctuation fields of these models converge to the stationary energy solution to a stochastic Burgers equation. The proof relies on a degeneration result of four basic beta-gamma models to the stationary O'Connell-Yor model for which the same equation has been recently derived by M. Jara and G. Moreno Flores.
Bruno Hideki Fukushima-Kimura (Hokkaido University)
Title:
Simulated Annealing for SCA: Results and new perspectives
Abstract:
One of the approaches adopted to solve certain combinatorial problems is to map such a problem into another one that consists of finding the minimizers of a Hamiltonian for an associated spin system. In our project we seek for an alternative stochastic algorithm other than Glauber and Metropolis dynamics that would give us a faster convergence to the ground states of the Hamiltonan. In this talk we show that by introducing a stochastic parallel dynamics in the spin system, the so-called SCA dynamics, there is a cooling temperature schedule under which such a dynamic will converge to the uniform distribution supported on the ground states, moreover, at fixed high temperatures the mixing time of the SCA dynamics is of order log(|V|). In the end we will discuss about ongoing results that would provide concrete applications in the real world.
Sosuke Ito (The university of Tokyo)
Title:
The projection theorem in information geometry and the entropy production
Abstract:
In this talk, we review a differential geometric method of information theory called information geometry and its application to statistical mechanics [1]. In information geometry, the Fisher information matrix gives a Riemannian metric, a dual pair of affine connections is defined, and the set of probabilities gives the manifold. We here show that the entropy production for the master equation is given by the projection onto the submanifold, which is related to the detailed balance condition.
[1] Sosuke Ito, Masafumi Oizumi, and Shun-ichi Amari, “Unified framework for the entropy production and the stochastic interaction based on information geometry” Phys. Rev. Research 2, 033048 (2020).
Hosho Katsura (The university of Tokyo)
Title:
Onsager's scars in non-integrable spin chains
Abstract:
The algebraic construction of the eigenstates of a Hamiltonian (or other conserved charges) is at the heart of quantum integrable models. Usually, this fails miserably in non-integrable models. However, recent studies on quantum many-body scar (QMBS) states have revealed a class of non-integrable models in which towers of exact eigenstates are built up by repeatedly acting with a certain "creation operator" on a simple (low-entanglement) state. Examples of such models include the Affleck-Kennedy-Lieb-Tasaki and the spin-1 XY models [1,2]. The eigenstates constructed this way have low entanglement even though their energies are in the middle of the spectrum, and thus violate the strong Eigenstate Thermalization Hypothesis (ETH). In this talk, I will show that an infinite sequence of non-integrable models with QMBS can be constructed using the so-called Onsager algebra [3]. Interestingly, this construction allows for the Hamiltonian to be spatially inhomogeneous. I will also show that the dynamics from a special class of initial states exhibits persistent many-body revivals. If time permits, I will talk about another algebraic approach to construct a class of models with QMBS.
[1] S. Moudgalya, N. Regnault, and B. A. Bernevig, PRB 98, 235156 (2018).
[2] M. Schecter and T. Iadecola, Phys. Rev. Lett. 123, 147201 (2019).
[3] N. Shibata, N. Yoshioka, and H. Katsura, Phys. Rev. Lett. 124, 180604 (2020).
Chihiro Matsui (The university of Tokyo)
Title:
Nonequilibrium physics of the XXZ model and spin-flip non-invariant conserved quantities
Abstract:
Recently found spin-flip non-invariant (SFNI) conserved quantities play important roles in discussing nonequilibrium physics of the XXZ model. The representative examples are the generalized Gibbs ensemble (GGE) and the ballistic transport of the spin current. In spite of big progress in understanding nonequilibrium physics of integrable systems, the general framework to determine a complete set of conserved quantities which describes the long-time steady state has not yet been found. In my talk, I discuss the complete GGE of the gapless XXZ model, which consists of functionally independent extensive conserved quantities. At the same time, the physical meaning of SFNI conserved quantities is partially provided. I also discuss that there exist ballistic channels of the spin current supported by non-quasilocal conserved quantities. The saturation of the lower bound for the Drude weight by quasilocal conserved quantities reads the linear dependence of non-quasilocal conserved quantities on quasilocal ones. I show that their (generalized) linearly dependence relation is consistent with the statement that the GGE consists of functionally independent conserved quantities without containing all linearly independent conserved quantities.
Yu Nakayama (Rikkyo University)
Title:
A review of the conformal bootstrap approach to three-dimensional critical Ising model
Abstract:
I will review a recent attempt to solve the three-dimensional critical Ising model from the conformal bootstrap, which gives the word record number. It is not entirely rigorous at this point, but some ingredients are rigorous or can be made rigorous. I hope that the conformal bootstrap program will become rigorous in the near future.
Ken Shiozaki (Kyoto University)
Title:
Topology of matrix product states with onsite symmetry
Abstract:
Motivated by Kitaev's proposal on the global structure of the space of short-range entangled states, we discuss the topological nature of the space of matrix product states with onsite symmetry.
Naoto Shiraishi (Gakushuin University)
Title:
Proof of absence of local conserved quantity in some nonintegrable models
Abstract:
The integrable system is one of the most important subjects in mathematical physics, and various models have been revealed to be integrable. Integrable systems possess sufficiently many local conserved quantities, which lies behind the solvability of integrable systems.
Although vast literature is devoted to integrability, very few studies have addressed non-integrability of concrete models. Here, we used the word “non-integrable” in the sense that the model has no local conserved quantity. The absence of local conserved quantities is relevant to various physical property. For example, it is necessary for thermalization and mixing. In spite of this necessity, the non-integrability of a certain model is usually not proven but only expected with some numerical supports. In fact, a rigorous proof of non-integrability in a concrete model has been completely elusive.
To break this impasse, in this talk, we rigorously prove that a particular quantum many-body system, the spin-1/2 XYZ chain with a magnetic field, is indeed non-integrable in the sense that this system has no nontrivial local conserved quantity [1]. The proof of non-integrability exploits a bottom-up approach: We first list up all the candidates of local conserved quantities, and then prove that all of them cannot be conserved. Any nontrivial conserved quantity in this model (except the Hamiltonian itself) turns out to be a sum of operators supported by at least half of the entire system. Our approach can apply to other S=1/2 systems including the Heisenberg model with the next nearest-neighbor interaction [2]. If we have a time, we briefly comment on the treatment for this case.
[1] N. Shiraishi, Europhys. Lett. 128 17002 (2019)
[2] N. Shiraishi, in preparation
Yohei Tanaka (Shinshu University)
Title:
Supersymmetric Index for Non-unitary Quantum Walks with Gapless Time-evolution
Abstract:
Recent developments in the mathematical study of discrete-time quantum walks allow us to assign a certain well-defined supersymmetric index to each pair $(U,\varGamma)$ of a unitary time-evolution $U$ and a $\mathbb{Z}_2$-grading operator $\varGamma$ satisfying the chiral symmetry condition $U^* = \varGamma U \varGamma.$ In this talk, I will explain how this index theory can be extended to encompass non-unitary $U$. The existing literature for unitary $U$ makes use of the indispensable assumption that $U$ is essentially gapped; that is, we require that the essential spectrum of $U$ contains neither $-1$ nor $+1$ to define the associated index. It turns out that this is no longer the case, if the given time-evolution $U$ is non-unitary. As a concrete example, we shall consider the time-evolution $U$ of a well-known non-unitary quantum walk model on the one-dimensional integer lattice $\mathbb{Z},$ introduced by Kim-Mochizuki-Obuse. This is joint work with Y. Matsuzawa, K. Asahara, D. Funakawa, M. Seki
Rongfeng Sun (National University of Singapore)
Title:
The two-dimensional continuum random field Ising model
Abstract:
In this talk, I will explain how to construct the two-dimensional continuum random field Ising model via scaling limits of a random field perturbation of the critical two-dimensional Ising model with diminishing disorder strength. Almost surely with respect to the continuum random field given by a white noise, the law of the magnetisation field is singular with respect to that of the two-dimensional continuum pure Ising model constructed by Camia, Garban and Newman. Based on joint work with Adam Bowditch.
Takato Yoshimura (Tokyo Institute of Technology )
Title:
Universal thermal transport in TTbar-deformed conformal field theories
Abstract:
In this talk I will discuss the universal properties of thermal transport in conformal field theories that are perturbed by an irrelevant operator TTbar. TTbar-deformation is known to be an exactly solvable deformation in that the spectrum of the undeformed theory alone suffices to predict that of the deformed theory. Unique properties of TTbar deformation allow us to study the TTbar-deformed CFTs using two disparate methods: integrability and holography. I will apply these two approaches to study the non-equilibrium steady states and Drude weights, finding perfect agreement. I will also discuss a curious connection between TTbar-deformed CFTs and an integrable cellular automaton model called the Rule 54 chain.