Spring 2022 Archive

Abstract: I will present recent extensions of neural-network quantum states [1] to interacting many-body systems with fermionic degrees of freedom.

Several complementary approaches will be shown, with applications to electronic structure of molecules [2], nuclear matter [3], as well as recent results

on the 2d Hubbard model [4].

[1] Carleo and Troyer, Science 355, 602 (2017)

[2] Choo, Mezzacapo, and Carleo, Nat. Comm. 11, 2368 (2020)

[3] Adams, Carleo, Lovato, and Rocco, Phys. Rev. Lett. 127, 022502 (2021)

[4] Robledo Moreno, Carleo, Georges, and Stokes, arXiv:2111.10420 (2021)

Abstract: In this talk, I will discuss our study on the exact RG flow of the O(N) vector model using nonperturbative quantum RG approach. We show that the beta functions in the entire coupling space are highly constraint and can be expressed in terms of beta functions defined in the subspace of couplings. Then, following the RG flow, I will present how to get the IR effective action of this O(N) model.

Abstract: In the last two decades the field of nonequilibrium quantum many-body physics has seen a rapid development driven, in particular, by the remarkable progress in quantum simulators, which today provide access to dynamics in quantum matter with an unprecedented control. However, the efficient numerical simulation of nonequilibrium real-time evolution in isolated quantum matter still remains a key challenge for current computational methods especially beyond one spatial dimension. In this talk I will present a versatile and efficient machine learning inspired approach. I will first introduce the general idea of encoding quantum many-body wave functions into artificial neural networks. I will then identify and resolve key challenges for the simulation of real-time evolution, which previously imposed significant limitations on the accurate description of large systems and long-time dynamics. As a concrete example, I will consider the dynamics of the paradigmatic two-dimensional transverse field Ising model, where we demonstrate that the reached time scales are comparable to or exceed the capabilities of state-of-the-art tensor network methods.

Abstract: The interplay of quantum fluctuations and interactions can yield to novel quantum phases of matter with fascinating properties. Understanding the physics of such system is a very challenging problem as it requires to solve quantum many body problems—which is generically exponentially hard on classical computers. In this context, universal quantum computers are potentially an ideal setting for simulating the emergent quantum many-body physics. Here we discuss two applications to the study of topologically ordered systems: First, we represent the ground states of Hamiltonians using shallow quantum circuits and observe a quantum phase transition between different symmetry-protected topological phases on a quantum device. Moreover, we present results for the realization of the topological Haldane phase with Fermi-Hubbard ladders in an ultracold-atom quantum simulator. Second, we prepare the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measure a topological entanglement entropy near the expected value of ln(2), and simulate anyon interferometry to extract the braiding statistics of the emergent excitations.

Abstract: Recent experimental advances, both in solids as well as quantum simulators, allow unprecedented microscopic studies of the structure of strongly correlated quantum matter. In the Fermi-Hubbard model, believed to underly high-Tc superconductivity, this allows to revisit a decades-old idea that strongly interacting electrons may fractionalize into partons — loosely speaking, the analogs of quarks in high-energy physics — called spinons and chargons. In this talk I will give an overview of recent theoretical and experimental results supporting this idea. A particular focus will be on dynamical signatures of meson formation in different experimentally relevant settings. First I will discuss multi-stage dynamics of quasiparticle formation when individual dopants are released from a pinning potential. I will show how the internal structure of the emerging charge carrier can be visualized by analyzing individual snapshots ofthe many-body wavefunction. In the second part of the talk, I will go beyond a single charge carrier and present a strong string-based pairing mechanism of holes which has recently led to the direct observation of hole-pairing in ultracold atoms. Finally I will discuss spectroscopic signatures of meson formation which provide a promising direction for future experiments, further extending the unprecedented microscopic insights into strongly correlated quantum matter afforded by quantum simulation experiments.

Abstract: Tensor networks are a set of tools and ideas developed for the efficient study of quantum many-body systems, where they provide a form of entanglement-based representations for quantum states. More fundamentally, however, tensor networks can also be viewed as a form data structure useful for representing certain types of correlated data. They possess many similarities to ideas developed in the context of data science in areas such as data classification, data compression and data completion.

In this talk I will provide an introduction to tensor networks, before describing recent work in which tensor networks are applied to produce more efficient algorithms for image compression (arXiv:220302556) and upcoming work in which tensor-based methods can be applied to the task of data completion; here completing a ground state wavefunction with high fidelity when only starting from a random partial sample.

Abstract: Quantum spin liquids (QSL) are enigmatic phases of matter characterized by the absence of symmetry breaking and the presence of fractionalized quasiparticles. While theories for QSLs are now in abundance, tracking them down in real materials has turned out to be remarkably tricky. I will present our recent work on candidate QSLs in three-dimensional frustrated pyrochlore systems [1,2,3], which benefited from determination of accurate material-specific effective model Hamiltonians. These Hamiltonians required a careful comparison with neutron scattering, magnetization and specific heat experiments and employed quantum and classical many-body techniques that were instrumental in explaining their findings. I will discuss the example of one such investigation in the context of Ce2Zr2O7 whose magnetic properties emerge from interacting cerium ions, and whose ground state "dipole-octupole" doublet (with J = 5/2,m_J = ±3/2) arises from strong spin-orbit coupling and crystal field effects. Our numerically determined effective Hamiltonian suggests the realization of a U(1) π-flux QSL phase [3] and allows us to make predictions for responses in an applied magnetic field that highlight the important role played by octupoles in the disappearance of spectral weight. Motivated by the questions that arise in the first part of the talk, the second part will take a broader viewpoint and will attempt to bridge the gap between the world of materials and models. In particular, I will pose the problem of effective model Hamiltonian determination precisely using the language of many-body wavefunctions, a desirable feature for strongly correlated systems. I offer a solution in the form of the "density matrix downfolding" technique [4,5], a form of Hilbert space operator renormalization.

Abstract: The density matrix renormalization group works because of the area law of the entanglement entropy. When using DMRG in electronic structure, a non-local basis can artificially give an area law ground state a volume law entropy. Here we report on two approaches to generating localized bases for use with DMRG. Along with reduced entanglement, the localized bases also generate diagonal two-electron interaction Hamiltonians, greatly improving the computational scaling. A sliced basis uses a grid in one dimension with gaussian bases in the two transverse directions. Gausslet bases utilize a distorted 3D grid, where at every gridpoint a special wavelet-inspired basis function produces the diagonal property. I will report on our latest developments in these areas.

Abstract: We construct a field-theoretic description of spin waves in hexagonal antiferromagnets with three magnetic sublattices and coplanar 1200 magnetic order [1]. The three Goldstone modes can be separated by point-group symmetry into a singlet α0 and a doublet β. The α0 singlet is described by the standard theory of a free relativistic scalar field. The field theory of the β doublet is analogous to the theory of elasticity of a two-dimensional isotropic solid with distinct longitudinal and transverse “speeds of sound.” The speeds of sound can be readily calculated for any lattice model. We apply this approach to the compounds of the Mn3X family with stacked kagome layers and extract the exchange coefficients for a model spin Hamiltonian by fitting to neutron scattering data [2]. We then extend our studies to the case of strained system where we show that strain can be used to tune the magnetism and the Hall response of these compounds in both static and dynamic conditions [3].

[1] S. Dasgupta and O. Tchernyshyov, Phys. Rev. B 102, 144417 (2020)
[2] Y. Chen et al Phys. Rev. B 102, 054403 (2020)
[3] S. Dasgupta, O. Tretiakov, Phys Rev Lett (in review)

Abstract: Though the cubic anisotropy is quite common in nature, spin systems with this anisotropy do not seem to have been studied so intensively, compared to countless publications on its isotropic counterpart. One of the reasons for this may be that we usually do not expect anything fancier about this system than the old problem concerning the lower-critical dimension for the cubic fixed point [1]. Another reason, though not so widely appreciated, may be the technical difficulty; there has been no algorithm that works. It is relatively easy to construct an algorithm for quantum Monte Carlo simulation with no negative signs, following the general prescription of local/loop/cluster updates, that can work in principle for the Heisenberg model with cubic spin anisotropy. However, as soon as we start simulation, we get stuck. To my knowledge, there is no QMC algorithm that works in practice. Recently, we carried out tensor network calculation of the model, and established the phase diagram for the S=2 model [2]. The phase diagram we obtained qualitatively agree with the mean-field analysis by Dom\'anski and Sznajd [3]. We also found a peculiar non-interacting quantum transition point where two cubic transition lines intersect. While the point itself is trivial (a product state), the system exhibits emergent U(1) symmetry in its vicinity, and the correlation length diverges towards this point.


  • [1] For example, H. Kleinert, S. Thoms and V. Schulte-Frohlinde, Phys. Rev. B 56 14428 (1997), and J. M. Carmona, A. Pelissetto and E. Vicari, Phys. Rev. B 61 (15136).

  • [2] W.-L. Tu, S. R. Ghazanfari, H.-K. Wu, H.-Y. Lee and N. Kawashima: arXiv:2204.01197.

  • [3] Z. Dom\'anski and J. Sznajd, J. of Magn. Magn. Mat. 71, 306 (1988).

Abstract: In the Hayden-Preskill protocol, which was proposed as a toy model for studying the black hole information loss problem from a quantum information theoretical viewpoint, black holes and their Hawking radiation are treated as composed of quantum bits. For an old black hole entangled with much Hawking radiation, an observer with the knowledge of the details of the black hole and the previous radiation would be able to gain the knowledge on new quantum information thrown into the black hole just by collecting new radiation of a similar amount. This information recovery is due to the scrambling dynamics of the quantum chaotic black hole and can be regarded as an information theoretical characterization of scrambling. We have quantitatively studied the relationship between the chaotic dynamics by quantum many-body Hamiltonian and quantum error correction accuracy [2]. In this talk, we discuss the cases of the Sachdev-Ye-Kitaev model and its two variants, namely the SYK4+2 model [3], in which the chaotic behavior is suppressed, and a version [4] of the sparse SYK model [5] where the absolute value of the couplings is limited to a constant.

  • [1] P. Hayden and J. Preskill, JHEP 0709, 120 (2007)[arXiv:0708.4025][2] B. Yoshida and A. Kitaev, arXiv:1710.03363.

  • [2] Y. Nakata and M. Tezuka, in preparation.

  • [3] see e.g. A. M. García-García, B. Loureiro, A. Romero-Bermúdez, and M. Tezuka, Phys. Rev. Lett. 120, 241603 (2018) [arXiv:1707.02197]; F. Monteiro, T. Micklitz, M. Tezuka, and A. Altland, Phys. Rev. Research 3, 013023 (2021) [arXiv:2005.12809]; F. Monteiro, M. Tezuka, A. Altland, D. A. Huse, and T. Micklitz, Phys. Rev. Lett. 127, 030601 (2021) [arXiv:2012.07884].

  • [4] M. Tezuka et al., in preparation.

  • [5] B. Swingle, talk at Workshop: Applications of Random Matrix Theory to Many-Body Physics (2019) ; S. Xu, L. Susskind, Y. Su, and B. Swingle, arXiv:2008.02303; A. M. García-García, Y. Jia, D. Rosa, and J. J. M. Verbaarschot, Phys. Rev. D 103, 106002 (2021) [arXiv:2007.13837].

  • Date: 6/8/2022 (Wednesday)

  • Time: 10:30 (Taipei time),

  • Venue: Zoom [Registration] is required

  • Zoom link: https://us02web.zoom.us/j/82485760144?pwd=WjhaVHplU2hvd0JJV2gvYU82MVFWdz09

  • Speaker: Wen-Han Kao (University of Minnesota)

  • Host: Prof. Yi-Ping Huang (Department of Physics, NTHU)

  • Title: Spin- and Flux-gap Renormalization in the Random Kitaev Spin Ladder

  • Abstract: We study the Kitaev spin ladder with random couplings by using the real-space strong-disorder renormalization group (SDRG) technique. This model is the minimum model in Kitaev systems that has conserved plaquette fluxes, and its quasi-one-dimensional geometry makes it possible to study the strong-disorder fixed points for both spin and flux excitations. In the Ising limit, the behavior of the spin gap is consistent with the familiar random transverse-field Ising chain with accessible analytic solutions, but the flux gap is dominated by the additional y-couplings. In the XX limit, while the x- and y-couplings are renormalized simultaneously, the z-couplings are not renormalized drastically and lead to non-universal disorder criticality at low-energy scales. Our work points out a new complexity in understanding the strong-disorder effect in frustrated spin systems with local conserved quantities.

  • Date: 6/15/2022

  • Time: 10:00 (Taipei time)

  • Venue: Zoom [Registration] is required

  • Zoom link: https://us02web.zoom.us/j/88285917510?pwd=T1FYL092MGtVbG4vVUJjLzQxa295QT09

  • Speaker: Akio Tomiya (Department of Information Technology, International Professional University of Technology)

  • Host: Prof. David Lin (Institute of Physics, NYCU)

  • Title: Schwinger model at finite temperature and density with classical-quantum hybrid algorithm.

  • Date: 8/3/2022

  • Time: 10:30 (Taipei time)

  • Venue: Zoom [Registration] is required

  • Zoom link: https://us02web.zoom.us/j/81286976921?pwd=Y2dBb2cwb2tmNFJ5U1BwUlMza2IyUT09

  • Speaker: Ching-Yao Lai (Princeton University )

  • Host: Prof. Ying-Jer Kao (Department of Physics, NTU)

  • Title: Physics-informed neural networks for fluid dynamics.

  • Abstract: Physics-informed neural networks (PINNs) have recently emerged as a new class of numerical solver for partial differential equations, leveraging deep neural networks constrained by equations. I'll discuss two applications of PINN in fluid dynamics developed in my group. The first concerns the search for self similar blow up solutions of the Euler equations. The second application uses PINN as an inverse method in geophysics. Whether an inviscid incompressible fluid, described by the 3-dimensional Euler equations can develop singularities in finite time is one of the most challenging problems in mathematical fluid dynamics (closely related to one of the seven Millennium Prize Problems). We employ PINN to discover a self-similar blow-up solution for the 3-dimensional Euler equations with a cylindrical boundary. This new numerical framework is shown to be robust and readily adaptable to other fluid equations. In the second part of the talk, I will discuss how PINNs trained with real world data from Antarctica can help discover flow laws that govern ice-shelf dynamics. Ice shelves play a crucial role in slowing glacier flow into the ocean which impacts the global sea-level rise. The flow of glaciers is governed by the ice viscosity, a crucial material property that cannot be directly measured. We used PINN to solve the governing equations for ice shelves and invert for its viscosity. Our calculation yields new flow laws of ice shelves that are different from commonly assumed in climate simulations, and suggests the need for reassessing the impact of our finding on the future projection of sea-level rise.