July 10 (Mon)

Time: 10:00 - 11:00 (1hours)

Title: Universality in Open Quantum Spin Chains with Non-Reciprocity

Abstract: We investigate the impact of non-reciprocity on universality and critical phenomena in open quantum systems. Non-reciprocal open quantum systems often have an exotic spectral sensitivity to boundary conditions, known as the Liouvillian skin effect (LSE). By considering an open quantum XXZ spin chain that exhibits LSE, we demonstrate the existence of a universal scaling regime that is not affected by the presence of the LSE. We resolve the critical exponents, which differ from those of free fermions, via tensor network methods and demonstrate that observables exhibit a universal scaling collapse. We find that the LSE only becomes relevant when a healing length scale at the system’s edge (which is different to the localization length of the eigenstate of the Liouvillian) exceeds the system size, allowing edge properties to dominate the physics. We expect this result to be a generic feature of non-reciprocal models with the LSE in the vicinity of a critical point.

Time: 11:15 - 12:15 (1hours)

Title: Weak-dissipation limit of the Liouvillian gap

Abstract: In recent years, open quantum many-body systems have received much attention due to experimental progress that allows us to introduce well-controlled dissipation to quantum many-body systems. A quantum Markov process is generated by the Liouvillian superoperator of the Lindblad form. An important quantity characterizing dissipative quantum dynamics is the Liouvillian gap, i.e., the spectral gap of the Liouvillian. The Liouvillian gap characterizes the asymptotic decay rate in the long-time regime. It was shown that a finite Liouvillian gap in the thermodynamic limit implies exponential decay of correlations in the steady state. As a consequence, a vanishing Liouvillian gap is used as a signature of a dissipative phase transition.  

In this talk, I focus on the Liouvillian gap of open quantum many-body systems in the weak dissipation limit. I argue that, counterintuitively, the thermodynamic limit of the Liouvillian gap in a chaotic open Floquet system (i.e., the Hamiltonian of the system of interest periodically depends on time) converges to a nonzero value in the weak dissipation limit. This nontrivial value of the Liouvillian gap is identified as the intrinsic decay rate of the underlying isolated quantum system. I also discuss an analogous result for open static systems, in which the Hamiltonian does not depend on time.

Time: 14:00 - 15:00 (1hours)

Title: Universality and breakdown of thermalization in isolated quantum systems

Abstract: Whether 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 via the eigenstate thermalization hypothesis (ETH) [2], recent studies show that thermalization can be prohibited by various mechanisms, such as many-body localization and quantum many-body scars. In this talk, we first discuss universality of thermalization in realistic quantum many-body systems. Although this problem has been investigated in terms of random matrix theory [3], conventional discussions fail in realistic systems with few-body interactions, which cannot be treated by standard random matrices [4]. To overcome this difficulty, we introduce ensembles of random Hamiltonians composed of few-body interactions as a model of generic realistic systems. Then, we numerically show that thermalization of realistic isolated quantum many-body systems is universal, unless the range of the interaction is not too long [5]. Next, we discuss additional constraints and symmetries affect thermalization of non-integrable systems. We start with high-dimensional quantum Ising model with a weak transverse field. Despite its non-integrability [6], domain-wall conservation law in this model leads to the Hilbert-space fragmentation, a recently found mechanism for the absence of thermalization. Then, we consider more general transverse-field Ising models that have discrete symmetry. In this case, while local observables satisfy the ETH, certain non-local observables break it due to the symmetry. We generalize this idea to systems with the higher-form symmetries, a newly recognized symmetries in high-energy physics. We show that the higher-form symmetries result in breakdown of the ETH for non-trivial non-local observables, which are verified in lattice Z2 gauge theory [7]. 

[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] J. v. Neumann, Zeit. Phys. 57, 30 (1929). [4] RH and M. Ueda, Phys. Rev. Lett. 120 (8), 080603 (2018). [5] S. Sugimoto, RH, and M. Ueda, Phys. Rev. Lett. 126 (12), 120602 (2021); Phys. Rev. Lett. 129 (3), 030602 (2022). [6] A. Yoshinaga, H. Hakoshima, T. Imoto, Y. Matsuzaki, and RH, Phys. Rev. Lett. 129 (9), 090602 (2022). [7] O. Fukushima and RH, arXiv:2305.04984 (2023).

July 11 (Tue)

Time: 10:00 - 11:00 (1hours)

Title: Advances through Computation in Chaotic Open Quantum Systems

Abstract: One of the most studied chaotic open quantum systems is almost as old as quantum mechanics itself: the compound nucleus. This nonhermitian many-body system has been instrumental in understanding quantum chaos and the ensuing universal behavior. Later the compound nucleus reemerged as a model for quantum dots and it was the starting point of the Sachdev-Ye-Kitaev model which is now the paradigm of many-body quantum chaos. In this talk I will start with an overview of open quantum systems and  emphasize the advances through computation in spite of the structural difficulties due to nonhermiticity. We discuss the effects of quantum chaos on phase transitions in nonhermtian systems and present recent work on relaxation using the Lindblad formalism.

Time: 11:15 - 12:15 (1hours)

Title: Classical and Quantum Variational Algorithms for Many-Body Physics

Abstract: With the recent advance of machine learning, variational quantum Monte Carlo (VQMC) with neural quantum states became a promising tool for solving the ground state problem of quantum many-body Hamiltonians. As the VQMC can estimate an observable without summing over the alternating signs, this method is often introduced as sign-free. In this talk, after introducing the algorithm, we unveil some hidden details of the method that still restricts it from solving Hamiltonians with strong sign problems. We especially argue that the expressivity of the network, which is often overlooked in studies, significantly limits its power. We also introduce a quantum counterpart of the algorithm, variational quantum eigensolver, and discuss how this method escapes the expressivity problem.

Time: 14:00 - 15:00 (1hours)

Title: Matrix product renormalization group

Abstract: We have proposed a new framework to solve various quantum many-body problems, which is named a matrix product renormalization group (MPRG) [1]. MPRG is one of the potential solutions to the sign problem of conventional Monte Carlo methods, and can be regarded as a generalization of a density matrix renormalization group (DMRG) in one dimension. Compared with DMRG, MPRG is directly applicable to infinite systems, higher-dimensional systems, finite-temperature systems, and even to open quantum systems. In particular, a nonvariational variant of MPRG can be used to simulate non-Hermitian models like the Yang-Lee model with a Yang-Lee edge singularity. A variational variant of MPRG has a further application to many Hermitian systems. By utilizing a continuous projected entangled pair state (cPEPS), we can even solve two-dimensional systems at finite temperature. As for the accuracy, cPEPS outperforms PEPS with about a one-digit-higher precision when the same bond dimension is used. The finite-temperature observables like a specific heat are also calculated and compared with a quantum Monte Carlo simulation. Due to the absence of a sign problem, a Trotter error, or a finite-size effect, the observables can easily be extrapolated to the thermodynamic limit only by the bond dimension scaling. [1] Masahiko G. Yamada et al., arXiv:2212.13267 (2022).

July 12 (Wed)

Time: 10:00 - 11:00 (1hours)

Title: An NQS+VMC study of the long-range antiferromagnetic Ising chain

Abstract: We study the quantum phase transition in the long-range (LR) antiferromagnetic (AF) Ising chain by using the variational Monte Carlo (VMC) method with the neural-network quantum state (NQS) ansatz. We employ the restricted Machine with complex-valued parameters as a NQS trial wave function for the VMC search for the groun state. The LR interactions are a power-law type with an experimentally tunable exponent, which has been a challenging subject of various numerical methods in the past decade. Nevertheless, the nature of the phase transition in the AF side at a small power-law exponent still remains less clear because of incomplete agreements between different numerical studies. In our study, from the identification of the standard critical exponents by performing phenomenological finite-size scaling (FSS) analysis, we find that the critical exponents agree well with the Ising universality class of the 2D classical Ising model regardless of the LR exponents examined, implying that the quantum-classical correspondence may still apply to the long-range AF interactions. In contrast, our test of the conformal field theory (CFT) descriptions shows clear deviation from the short-range Ising model at a small LR exponent. While the central charge provides less conclusive results on such deviation under periodic boundary conditions, the breakdown of the CFT descrption is evident with the test of the correlation function form when the exponent goes below 2. Our numerical results corroborate with the scenario proposed in the LR-interacting Kitaev chain where the LR interaction breaks the conformal symmetry while keeping the critical exponents of the short-range class.

Time: 11:15 - 12:15 (1hours)

Title: Partial deconfinement in theories, from large-N theories to SU(N=3) QCD

Abstract: The confinement/deconfinement phase transition of the gauge theories at finite temperature has been investigated intensively for a long time. In order to reveal its nonperturbative aspect, analyses taking the large-N limit provide several nontrivial properties. In particular, it has been discussed that the phase structure of the large-N gauge theories may be separated into three distinct phases characterized by two phase transitions, Hagedorn and Gross-Witten-Wadia transitions at large N. In this talk, we discuss the description of such phase characterization, mainly by using the Polyakov loop in several models, including BFSS-type matrix models. We will also explore the application of the picture and description based on the large-N nature to SU(N=3) QCD with fundamental quarks.

Time: 14:00 - 15:00 (1hours)

Title: Symmetry-restoring homotopic action for half-filled 2d Hubbard model

Abstract: We present the theory of symmetry-restoring homotopic action with the proof-of-principle example 2d Hubbard model. By explicitly breaking the existing symmetry of the original action at the reference system and expanding with respect to the symmetry-restoring and many-body interaction term, one can achieve the improved convergence in the diagrammatic series. Furthermore, we show that the freedom of choosing the dependence of the symmetry restoring term on the expansion parameter allows one to tame dangerous long-order oscillations, inherent in symmetry-restoring expansions, with controlled error bars. We access low-temperature strong-coupling regime of the half-filled 2d Hubbard model with large antiferromagentic correlation length, and observe the Slater- to-Mott Hubbard crossover in a numerically exact way.

Time: 15:00 - 15:15 (10min + 5min Q&A)

Title: TBA

Abstract: TBA

July 13 (Thu)

Time: 10:00 - 11:00 (1hours)

Title: Thimble computation of the IKKT matrix model

Abstract: The IKKT matrix model is an attractive candidate of non-perturbative formulation of superstring theory. A remarkable conjecture of the matrix model is that the SO(9,1) Lorentz symmetry is spontaneously broken and (3+1)-dimensional spacetime emerges out of matrix degrees of freedom. Since it is extremely difficult to prove the conjecture analytically, we resort to numerical techniques to show the spontaneous symmetry breaking. In this talk, we discuss a numerical Lefschetz thimble method and how it will overcome the sign problem, which appears in simulations of the matrix model. As a kick-start, we consider the bosonic part of the matrix model with an additional mass term and discuss its phase structure.

Time: 11:15 - 12:15 (1hours)

Title: Numerical methods in lattice field theory beyond the standard model

Abstract: Lattice field theory provides a non-perturbative regularization suitable for strongly interacting systems, which has proven crucial to the study of quantum chromodynamics among many other theories. Lattice investigations of potential new strong dynamics beyond the standard model of particle physics (BSM) encounter challenges that motivate the development and application of novel numerical methods. I will discuss examples from three areas of BSM lattice investigations: composite Higgs models based on near-conformal gauge theories, models of composite dark matter, and supersymmetric lattice field theories related to quantum gravity by holographic dualities.

Time: 14:00 - 15:00 (1hours)

Title: Fock space localization and quantum error correction in SYK-like models

Abstract: We will review the recent progress in our study of SYK-like models, obtained in several collaborations including the speaker, with emphasis on the numerical results and their implications. References: arXiv:2005.12809, 2012.07884, 2208.12098, and 2303.02010.