研究室メンバーによるレギュラー・セミナー、 および、他研究室・機関からのゲスト・スピーカーのセミナーを開催しています。 レギュラー・セミナーは下記要領で行います。

• 夏学期： 古典的論文のレヴューを行います。配布資料は英語、発表は英語もしくは日本語です。
  
• 冬学期： 研究結果の紹介もしくは研究に関係したレビューを行います。発表は英語です。

Access map：理学部1号館 (Faculty of Science Bldg. 1) / 理学部4号館 (Faculty of Science Bldg. 4)

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冬学期 / Winter semester (October 2021-January 2022)

   木曜日13時からZoom上で行います(普段と場所or時間の異なる場合は赤字で示します)。
    Each seminar starts from 13:00, Thursday via Zoom (unless otherwise indicated).
<Schedule>
Oct. 7 Joining of new B4 & M1 members
Oct. 14 Nakagawa
Oct. 21 Wang
Oct. 28 Matsumoto
Nov. 4 Sakamoto / Kawabata
Nov. 11 Mori
Nov. 18 Z. Liu
Nov. 25 K. Liu
Dec. 2 (No seminar)
Dec. 9 Sugimoto
Dec. 16 Dabelow
Dec. 23 Shiraishi
Jan. 6 Li
Jan. 13 Hara

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speaker	Masaya Nakagawa
title	Exact eigenstates and weak ergodicity breaking in multicomponent Hubbard models
abstract	The η-pairing state is an exact superfluid eigenstate of the Fermi-Hubbard model constructed by C. N. Yang [1]. In this work, we construct exact eigenstates of multicomponent Hubbard models, which include the SU(N) Hubbard model as a special case, by generalizing the η-pairing mechanism [2]. The generalized η-pairing eigenstates are formed through simultaneous condensation of multiple types of fermion pairs and shown to exhibit off-diagonal long-range order coexisting with magnetic long-range order. Unlike the two-component case, these exact eigenstates do not arise from symmetry of the Hamiltonian, but originate from a restricted spectrum-generating algebra supported by the Pauli exclusion principle. Building on this fact, we show that the generalized η-pairing eigenstates do not obey the eigenstate thermalization hypothesis and can be regarded as quantum many-body scar states. This result indicates that the N-component Hubbard models show weak ergodicity breaking for N ≧ 3. References: [1] C. N. Yang, Phys. Rev. Lett. 63, 2144 (1989). [2] M. Nakagawa, H. Katsura, and M. Ueda, in preparation.

speaker	Zhikang Wang
title	Measurement induced phase fixation in discrete space
abstract	We find that in a lattice space, the wave function of free particles develop a fixed relation of its complex phases at different sites when general continuous position measurement is present, and as a consequence, the expectation value of the energy becomes constantly zero at each single trajectory level, and the expection value of the energy cannot be perturbed by the stochastic measurement outcome. We discuss the properties and the generality of this result, and we show how this phase relation is developed, and discuss the conditions for developing this phase relation.

speaker	Norifumi Matsumoto
title	Quantum many-body scar states in a Rydberg-atom chain with hopping
abstract	Recently, unusual initial states have been experimentally discovered which does not reach the thermal equilibrium for an anomalously long time in contrast to the rapid thermalization of the majority of initial states[1]. Motivated by this result, intensive research has been conducted investigating quantum many-body scar states, which exhibit an extremely slow thermalization or even absence of it. In the system discussed in Ref.[1], atoms trapped in an optical lattice are described as two-level systems, in which the high-energy level, called the Rydberg state, exhibits a strong repulsion with neighboring ones. Here, to gain an insight into the emergence of quantum many-body scar states and thermalization, we investigate the situation in which there are unoccupied sites and atoms can hop between nearest-neighbor sites, while in the original study atoms are fixed at each site. Specifically, we numerically obtain the energy spectrum and eigenstates as well as their entanglement entropy for a small number of sites and atoms. We show the existence of a series of low-entangled states and analyze their property. Furthermore, we discuss their influence on the dynamics and an algebraic relationship among some of them. (This research is conducted in the self-directed joint-research project as a part of the course work of the leading graduate school MERIT.) [1]H. Bernien et al., Nature 551, 579 (2017).

speaker	Yuki Sakamoto
title	Game-Theoretical Models on a Graph
abstract	Game theory is commonly used to explain human decision-making processes and has an important role in economics, biology and other various fields. In this seminar, we would see a game-theoretical model with a large population on a graph and Pairwise-Fermi update rule. We mainly focus on what is called the prisoner's dilemma game, where two rational players are likely to mutually defect and fail to reach the optimal choices for both players. In this model, a phase transition behavior can be observed with respect to the coefficient of cost-to-benefit ratio and the strength of natural selection.

speaker	Kohei Kawabata
title	Nonlinear Landauer Formula
abstract	The Landauer formula provides a general scattering formulation of electrical conduction. Despite its utility, it has been mainly applied to the linear-response regime, and a scattering theory of nonlinear response has yet to be fully developed. Here, we extend the Landauer formula to the nonlinear-response regime. We show that while the linear conductance is directly related to the transmission probability, the nonlinear conductance is given by its derivatives with respect to energy. This sensitivity to the energy derivatives is shown to produce unique nonlinear transport phenomena of mesoscopic systems including disordered and topological materials. By way of illustration, we investigate nonlinear conductance of disordered chains and identify their universal behavior according to symmetry. In particular, we find large singular nonlinear conductance for zero modes, including Majorana zero modes in topological superconductors. We also show the critical behavior of nonlinear response around the mobility edges due to the Anderson transitions. Moreover, we study nonlinear response of graphene as a prime example of topological materials featuring quantum anomaly. Furthermore, considering the geometry of electronic wave functions, we develop a scattering theory of the nonlinear quantum Hall effect. We establish a new connection between the nonlinear quantum Hall response and the nonequilibrium quantum fluctuations. We also discuss the influence of disorder and Anderson localization on the nonlinear quantum Hall effect. Our work opens a new avenue in quantum physics beyond the linear-response regime. Reference: K. Kawabata and M. Ueda, arXiv:2110.08304

speaker	Takashi Mori
title	Heating in many-body systems under fast and strong driving
abstract	Heating under periodic driving is a generic nonequilibrium phenomenon, and it is a challenging problem in nonequilibrium statistical physics to derive a quantitatively accurate heating rate. Here, we provide a simple formula on the heating rate under fast and strong periodic driving in classical and quantum many-body systems. The key idea behind the formula is constructing a time-dependent dressed Hamiltonian by moving to a rotating frame, which is found by a truncation of the high-frequency expansion of the micromotion operator, and applying the linear-response theory to the dressed Hamiltonian, rather than the bare Hamiltonian. It is confirmed for specific classical and quantum models that the second-order truncation of the high-frequency expansion yields quantitatively accurate heating rates beyond the linear-response regime. Our result implies that the information on heating dynamics is encoded in the first few terms of the high-frequency expansion, although heating is often associated with an asymptotically divergent behavior of the high-frequency expansion. Reference: T. Mori, arXiv:2107.12587

speaker	Ziyin Liu
title	Stochastic Neural Networks with Infinite Width are Deterministic
abstract	In this work, we show the predictive variance of a trained stochastic neural network tends to zero as its width tends to infinity. Our results shed light on how stochastic neural networks work and have important implications for distribution modeling with neural networks and Bayesian deep learning.

speaker	Kangqiao Liu
title	An attempt to construct a quantum information engine on a tilted 1D periodic potential
abstract	Traditionally, people use Maxwell's demon to construct classical information engines by harnessing the thermal fluctuations. Recently, a minimal model of quantum information engine fueled by pure quantum measurements without the aid of a thermal bath has been proposed. It consists of a two-level system and work can be extracted by simply performing measurements on the qubit. We attempt to construct a quantum information engine in a tilted potential using measurement and feedback control. In this seminar, I'm going to review classical and quantum information engines, the Bloch oscillation, and then describe our problem setup.

speaker	Shoki Sugimoto
title	Eigenstate Thermalization in Long-Range Interacting Systems
abstract	Long-range interacting systems show many unique phenomena such as negative heat capacity, anomalous propagation of correlations, and prethermalization. Trapped-ion systems offer an ideal platform for investigating thermal and dynamical properties of systems with long-range interaction ~r -α with the ability to tune α from 0 to 3. Prethermalization of transverse Ising model with long-range interactions was experimentally observed, but a complete thermalization was not observed within an experimentally accessible time [1], suggesting a possible breakdown of the eigenstate thermalization hypothesis (ETH). The strong ETH states that every eigenstate of a quantum many-body system is thermal per se, and generic nonintegrable isolated quantum systems are believed to thermalize according to the strong ETH. The strong ETH has numerically been verified to hold for various short-range interacting systems. However, little is known about its validity in long-range interacting systems except for a few specific models. In our work [2], we construct a set of systems with two-body and tunable-range interactions and test the validity of the strong ETH for such systems, providing solid numerical evidence that the strong ETH typically holds for α ≧ 0.6. However, we find that long-range interactions make eigenstate expectation values significantly deviate from the microcanonical average, especially for finite-size systems used in experiments. We also find that Srednicki's ansatz typically breaks down for α ≦ 1.0. These results reveal an intermediate region where the strong ETH typically holds, but Srednicki's ansatz typically breaks down. References: [1] B. Neyenhuis, et al., Science Advances 3, 1700672 (2017) [2] S. Sugimoto, R. Hamazaki, and M. Ueda, arXiv:2111.12484 (2021)

speaker	Lennart Dabelow
title	Sampling Accuracy-Versus-Efficiency Tradeoff in Restricted Boltzmann Machines
abstract	Restricted Boltzmann Machines (RBMs) are a popular and versatile architecture for unsupervised machine learning, which can in principle approximate any target probability distribution with arbitrary accuracy. However, due to its computational complexity, the RBM model is usually not directly accessible, and Markov-chain sampling is required to analyze its distribution or to sample from it. For training and production, it is thus desirable to have a sampler that is both accurate and efficient. We highlight that these two goals generally compete with each other and cannot be achieved simultaneously. More specifically, we identify three regimes of RBM training: independent learning, where the accuracy can be improved without loss of efficiency; correlation learning, where higher accuracy entails lower efficiency; and degradation, where both accuracy and efficiency stall or even deteriorate. The findings are based on analytical arguments and ample numerical experiments.

speaker	Koki Shiraishi
title	Thermalization of locally dissipated open quantum many-body systems
abstract	How the statistical ensemble, which is assumed a priori in statistical mechanics, is derived at the microscopic level has been a matter of interest to physicists. Here, we will investigate the relaxation of states in open quantum systems into a statistical ensemble. The time evolution of quantum open systems is often described by the Lindblad equation. In the following, we will discuss how a locally dissipated quantum many-body system relaxes to a thermal equilibrium state under the time evolution described by the Lindblad equation. Previous studies have concluded that non-integrable systems reach thermal equilibrium with the Lindblad time evolution of local dissipation, but integrable systems do not.[1] In this seminar, we will discuss whether an integrable system, a one-dimensional free Boson chain, can reach thermal equilibrium when local dissipation is added. We will show numerically that it is indistinguishable from a thermal equilibrium state when looking at the energy distributions and the particle number distribution at each site. [1] Žnidarič et.al. PRE 81, 051135 (2010), Palmero et al. PRE 100, 022111 (2019)

speaker	Hongchao Li
title	Introduction to Non-equilibrium Green’s Function and Application
abstract	Understanding the quantum many-body physics problem is one of the grand challenges of modern physics. In thermodynamic equilibrium, the combined effort of experimental and theoretical research has made tremendous progress over the last decades. However, analogous scenarios and theoretical tools are much less developed. For thermodynamic-equilibrium cases, the usual time-ordered Green’s function on the Feynman contour or on the Matsubara contour still has its position. However, it fails in generally non-equilibrium situations. So the perturbation expansion for the non-equilibrium Green’s function is constructed and introduced to analyze the problems in non-equilibrium phases of quantum matter.[1] In this seminar, we will introduce the concepts of Schwinger-Keldysh contour and contour-ordered Green’s function(non- equilibrium Green’s function). We will then show the application of Green’s functions to transport problems such as anomalous quantum Hall effect and open quantum systems[2]. We will also introduce two ways of constructing non-equilibrium Green’s function and find the connections between them. [1] "An Introduction to Nonequilibrium Many-Body Theory" by Joseph Marciejko [2] L. M. Sieberer, M. Buchhold, and S. Diehl, Rep. Prog. Phys. 79, 096001 (2016)

speaker	Naoki Hara
title	Metastable ferromagnetic clusters in dissipative molecular systems
abstract	Having strong dipole-dipole interaction, ultracold polar molecules provide a highly tunable platform of quantum magnetism with long-range interaction, which cannot be realized with atomic systems [1]. However, since the chemical reaction of molecules causes them to be lost from the trap, it is fundamentally and practically important to take into consideration the effect of dissipation on quantum magnetism in molecular systems. Recently, it was shown that the introduction of dissipation reverses the sign of magnetic correlations from antiferromagnetic to ferromagnetic in ultracold atomic systems [2]. We have employed the similar treatment of dissipation to calculate the dynamics of molecular systems and observed the existence of metastable states stabilized by an interplay between long-range interaction and dissipation. These states have been found to be composed of a number of ferromagnetic clusters, which are unique to the many-body systems. [1] A. V. Gorshkov et al., Phys. Rev. A 84, 033619 (2011). [2] M. Nakagawa, N. Tsuji, N. Kawakami, and M. Ueda, Phys. Rev. Lett. 124, 147203 (2020).

で行います(普段と場所or時間の異なる場合は赤字で示します)。
    Each seminar starts from 13:00, Thursday via Zoom (unless otherwise indicated).

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夏学期 / Summer semester (April-July 21)

<Regular seminars (review of seminal papers)>
    木曜日13時からZoom上で行います(普段と場所or時間の異なる場合は赤字で示します)。
    Each seminar starts from 13:00, Thursday via Zoom (unless otherwise indicated).

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April 15 (Thu) Shoki Sugimoto
    "The second laws of quantum thermodynamics"
    F. Brandao, M. Horodecki, N. Ng, J. Oppenheim, and S. Wehner, Proc. Natl. Acad. Sci. U.S.A. 112, 3275 (2015)

April 22 (Thu) Norifumi Matsumoto
    "Coexistence of Diffusive and Ballistic Transport in a Simple Spin Ladder"
    M. Znidaric, Phys. Rev. Lett. 110, 070602 (2013)

May 6 (Thu) Ziyin Liu
    "Portfolio Selection"
    H. Markowitz, The Journal of Finance 7, 1, 77-91 (1952)
    "Empirical properties of asset returns: stylized facts and statistical issues"
    R. Cont, Quantitative Finance, 1, 223-236 (2001)

May 13 (Thu) Zhikang Wang
    "Bose-Einstein condensation in the alkali gases: Some fundamental concepts"
    A. J. Leggett, Rev. Mod. Phys. 73, 307 (2001)
    "Theory of Bose-Einstein condensation in trapped gases"
    F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999)

May 20 (Thu) (No seminar)

May 27 (Thu) (No seminar)

June 3 (Thu) Kohei Kawabata
    "Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model"
    F. D. M. Haldane, Phys. Lett. A 93, 464 (1983)
    "Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Neel State"
    F. D. M. Haldane, Phys. Rev. Lett. 50, 1153 (1983)

June 10 (Thu) Yuki Sakamoto
    "Non-Abelian anyons and topological quantum computation"
    Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, and Sankar Das Sarma, Rev. Mod. Phys. 80, 1083 (2008)
    "Introduction to topological quantum computation with non-Abelian anyons"
    Bernard Field and Tapio Simula, Quantum Sci. Technol. 3 045004 (2018)

June 17 (Thu) 12:30- Kangqiao Liu
    "The fluctuation-dissipation theorem"
    R. Kubo, Rep. Prog. Phys. 29 255 (1966)

June 24 (Thu) Hyuntae Moon
    "Simple mathematical models with very complicated dynamics"
    R. M. May, Nature 261, 459-467 (1976)

July 1 (Thu) Tatsuki Odake
    "Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer"
    P. W. Shor, SIAM J. Comput., 26(5), 1484-1509 (1997)
    "Algorithms for quantum computation: discrete logarithms and factoring"
    P. W. Shor, Proceedings 35th Annual Symposium on Foundations of Computer Science, pp. 124-134 (1994)

July 8 (Thu) Koki Shiraishi
    "A Gallavotti-Cohen-Type Symmetry in the Large Deviation Functional for Stochastic Dynamics"
    J. L. Lebowitz and H. Spohn, J. Stat. Phys. 95, 365 (1999)

July 15 (Thu) (No seminar)