イベント検索

Isometric tensor networks in two dimension

2022年10月11日(火) 10:30 - 12:00

ヤンタオ・ウー (理化学研究所 数理創造プログラム (iTHEMS) 特別研究員)

In this talk, I would like to explain the ansatz of isometric tensor network states (isoTNS) as candidate wavefunctions in two-dimensional condensed matter systems. I will explain how the isometric structure in 2D helps generalize many 1D tensor network algorithms, like the density matrix renormalization group and the time-evolution block decimation methods, to two dimensions. Both bosons and fermions; ground states and dynamics will be discussed. I will also explain why it is a friendly trial wavefunction in the context of variational Monte Carlo, where the sampling correlation time vanishes. I will also explain its relation to quantum error correction and how it provides an interesting playground of quantum information. If time permits, I would like to discuss some open questions about its representability of topological phases.

会場: コモンルーム (246-248号室) (メイン会場) / via Zoom

イベント公式言語: 英語

Transport coefficients of a Bose gas in one dimension

2022年10月5日(水) 13:30 - 15:00

西田 祐介 (東京工業大学 理学院 物理学系 准教授)

I will present two of our recent studies on transport coefficients of a Bose gas in one dimension. The first part is on the thermal conductivity [1], which is typically divergent for quantum integrable systems in one dimension. However, it is found to be finite and dominated by an effective three-body interaction that inevitably arises by confining bosons into a tight matter waveguide. The second part is on the bulk viscosity [2], which is computed perturbatively in the high-temperature, weak-coupling, and strong-coupling limits. In particular, the strong-coupling limit is accessible thanks to the Bose-Fermi duality, which is shown for the dynamic bulk viscosity provided by the contact-contact response function.

会場: via Zoom

イベント公式言語: 英語

Phantom Bethe excitations and spin helices in integrable spin chains

2022年9月15日(木) 17:00 - 18:15

Vladislav Popkov (University Wuppertal, Germany)

We demonstrate the existence of a special chiral “phantom” mode with some analogy to a Goldstone mode in the anisotropic quantum XXZ Heisenberg spin chain. The phantom excitations contribute zero energy to the eigenstate, but a finite fixed quantum of momentum. The mode exists not due to symmetry principles, but results from nontrivial scattering properties of magnons with momentum k given by the anisotropy via cos (k) = Jz/Jx. The mode originates from special string-type solutions of the Bethe ansatz equations with unbounded rapidities, the phantom Bethe roots. All such Bethe states are chiral (the simplest representative being factorized state with helicoidal magnetization profile) and exist in both periodic and open XXZ spin chain under fine-tuning. I show how phantom Bethe states can be generated dissipatively, by setting a polarization gradient via coupling the ends of the open spin chain to suitable dissipative baths. Spin helix eigenstates were observed and used in recent cold atom experiments, and led to further surprising findings.

会場: via Zoom

イベント公式言語: 英語

From the Black Hole Conundrum to the Structure of Quantum Gravity

2022年7月26日(火) 15:30 - 17:00

野村 泰紀 (Professor/Director, Berkeley Center for Theoretical Physics, University of California, Berkeley, USA)

Having a complete quantum theory of gravity has long been a major goal of theoretical physics. This is because a naive merger of quantum mechanics and general relativity — though it works in certain limited regimes — suffers from major theoretical problems. A particularly acute one arises when one considers the quantum mechanics of black holes: two fundamental principles of modern physics — the conservation of probability in quantum mechanics and the equivalence principle of general relativity — seem to be incompatible with each other. I will explain how recent theoretical progress begins to address this problem and portray the emerging picture of how spacetime and gravity behave at the level of full quantum gravity.

会場: 理化学研究所 和光キャンパス RIBF棟 2階 大会議室 / via Zoom

イベント公式言語: 英語

Superconducting-like heat current: Effective cancellation of current-dissipation trade-off by quantum coherence

2022年7月25日(月) 13:30 - 15:00

田島 裕康 (電気通信大学 大学院情報理工学研究科 助教)

Recent developments in statistical mechanics have revealed a tradeoff between heat current and dissipation [1,2]. In various situations, this current-dissipation tradeoff represents a relationship between thermal energy flow and entropy increase, similar to Joule’s law W=RI^2. On the other hand, the coherence effect on the current-dissipation tradeoff has not been thoroughly analyzed. Here, we systematically analyze how coherence affects the current-dissipation tradeoff [3]. The results can be summarized in the following three rules:

会場: via Zoom

イベント公式言語: 英語

Speed limits for macroscopic transitions

2022年7月13日(水) 13:30 - 15:00

濱崎 立資 (理化学研究所 開拓研究本部 (CPR) 濱崎非平衡量子統計力学理研白眉研究チーム 理研白眉研究チームリーダー)

Speed of state transitions in macroscopic systems is a crucial concept for foundations of nonequilibrium statistical mechanics as well as various applications in quantum technology represented by optimal quantum control. While extensive studies have made efforts to obtain rigorous constraints on dynamical processes since Mandelstam and Tamm, speed limits that provide tight bounds for macroscopic transitions have remained elusive. Here, by employing the local conservation law of probability, the fundamental principle in physics, we develop a general framework for deriving qualitatively tighter speed limits for macroscopic systems than many conventional ones. We show for the first time that the speed of the expectation value of an observable defined on an arbitrary graph, which can describe general many-body systems, is bounded by the “gradient” of the observable, in contrast with conventional speed limits depending on the entire range of the observable. This framework enables us to derive novel quantum speed limits for macroscopic unitary dynamics. Unlike previous bounds, the speed limit decreases when the expectation value of the transition Hamiltonian increases; this intuitively describes a new trade-off relation between time and the quantum phase difference. Our bound is dependent on instantaneous quantum states and thus can achieve the equality condition, which is conceptually distinct from the Lieb-Robinson bound. We also find that, beyond expectation values of macroscopic observables, the speed of macroscopic quantum coherence can be bounded from above by our general approach. The newly obtained bounds are verified in transport phenomena in particle systems and nonequilibrium dynamics in many-body spin systems. We also demonstrate that our strategy can be applied for finding new speed limits for macroscopic transitions in stochastic systems, including quantum ones, where the bounds are expressed by the entropy production rate. Our work elucidates novel speed limits on the basis of local conservation law, providing fundamental limits to various types of nonequilibrium quantum macroscopic phenomena.

会場: コモンルーム 246-248号室 とZoomのハイブリッド開催

イベント公式言語: 英語

Adiabatic pumps in quantum spin systems

2022年7月12日(火) 16:00 - 17:15

塩崎 謙 (京都大学 基礎物理学研究所 助教)

The Thouless pump is a one-parameter cycle of 1-dimensional gapped quantum systems with U(1) symmetry, which is classified by integers. In this talk, I introduce a generalization of the Thouless pump to quantum spin systems in any dimension with any finite group onsite symmetry. I show a simple model with Z_2 onsite symmetry, and how it is nontrivial via boundary degrees of freedom. Using the framework of the injective matrix product state, one can construct the topological invariant in a way similar to the Berry phase. If time allows, I will briefly introduce a group cohomology model by Roy and Harper for generic space dimensions and discuss its properties.

会場: via Zoom

イベント公式言語: 英語

Gradient flow exact renormalization group 2

2022年7月6日(水) 13:30 - 17:00

鈴木 博 (九州大学 大学院理学研究院 教授)

Wilson’s exact renormalization group (ERG), which tells how a system changes under the scale transformation, provides a fundamental framework to define quantum field theory even beyond the perturbation theory. It has however been known that it is difficult to preserve a manifest gauge symmetry in ERG because of the usage of the momentum cutoff in ERG. Here, we propose a possible modification of ERG, the gradient flow exact renormalization (GFERG), which preserves a manifest gauge symmetry being based on a gauge-covariant diffusion equation. I explain the basic idea and properties of GFERG. If time permits, I want to present a possible application of GFERG to the consideration of the axial anomaly.

会場: via Zoom

イベント公式言語: 英語

Gradient flow exact renormalization group 1

2022年7月5日(火) 13:30 - 17:00

鈴木 博 (九州大学 大学院理学研究院 教授)

Wilson’s exact renormalization group (ERG), which tells how a system changes under the scale transformation, provides a fundamental framework to define quantum field theory even beyond the perturbation theory. It has however been known that it is difficult to preserve a manifest gauge symmetry in ERG because of the usage of the momentum cutoff in ERG. Here, we propose a possible modification of ERG, the gradient flow exact renormalization (GFERG), which preserves a manifest gauge symmetry being based on a gauge-covariant diffusion equation. I explain the basic idea and properties of GFERG. If time permits, I want to present a possible application of GFERG to the consideration of the axial anomaly.

会場: via Zoom

イベント公式言語: 英語

Topological quantum effects in low-dimensional spin systems - The power of the boundary

2022年6月30日(木) 17:00 - 18:15

Thore Posske (Group Leader, I. Institute for Theoretical Physics, University of Hamburg, Germany)

Manipulating the boundary of low-dimensional magnetic structures could grant control about topological magnetic quantum sates. I will discuss the creation of one- and two-dimensional topological quantum magnets by manipulating the boundary magnetization, address their stability against external perturbations, and discuss their possible application to quantum information processing.

会場: via Zoom

イベント公式言語: 英語

Topological aspects of non-Hermitian physics

2022年6月21日(火) 16:00 - 17:15

大熊 信之 (京都大学 基礎物理学研究所 助教)

The past decades have witnessed an explosion of interest in topological materials, and a lot of mathematical concepts have been introduced in condensed matter physics. Among them, the bulk-boundary correspondence is the central topic in topological physics, which has inspired researchers to focus on boundary physics. Recently, the concepts of topological phases have been extended to non-Hermitian Hamiltonians, whose eigenvalues can be complex. Besides the topology, non-Hermiticity can also cause a boundary phenomenon called the non-Hermitian skin effect, which is an extreme sensitivity of the spectrum to the boundary condition. In this talk, I will explain recent developments in non-Hermitian topological physics by focusing mainly on the boundary problem. As well as the competition between non-Hermitian and topological boundary phenomena, I will discuss the topological nature inherent in non-Hermiticity itself. Field: condensed matter physics Keywords: topological materials, non-Hermitian systems, skin effect, bulk-boundary correspondence

会場: via Zoom

イベント公式言語: 英語

Introduction to Topological Insulators: The Ten-fold Classification of Topological Insulators and Superconductors Part.2

2022年6月13日(月) 14:00 - 15:30

邱 靖凱 (理化学研究所 数理創造プログラム (iTHEMS) 上級研究員)

会場: via Zoom

イベント公式言語: 英語

Introduction to Topological Insulators: The Ten-fold Classification of Topological Insulators and Superconductors Part.1

2022年5月24日(火) 14:00 - 15:30

邱 靖凱 (理化学研究所 数理創造プログラム (iTHEMS) 上級研究員)

会場: via Zoom

イベント公式言語: 英語

A mathematical formulation of two-dimensional conformal field theory

2022年5月23日(月) 14:00 - 16:30

森脇 湧登 (理化学研究所 数理創造プログラム (iTHEMS) 基礎科学特別研究員)

The mathematical construction of non-trivial quantum field theory in four dimensions, known as the "Yang-Mills existence and mass gap problem", is a very important issue in mathematical sciences. There are many examples of rigorous quantum field theories in two dimensions, although the four dimensions have not yet been solved. In particular, two-dimensional conformal field theory, which is a quantum field theory with conformal symmetry, has good properties and can be formulated mathematically using algebraic structures formed by "products of a field and a field" (operator product expansion). In this talk, this algebraic formulation (full vertex algebra) will be explained. Various construction methods and concrete examples (construction using codes, construction from quantum groups, and construction by deformation) will then be discussed. All the talk here is mathematical, but I will try to speak in a way that is motivated by physics as much as possible throughout the talk. I hope to receive various comments from the viewpoints of other fields.

会場: コモンルーム 246-248号室 とZoomのハイブリッド開催

イベント公式言語: 英語

Recent Progress in the Swampland Program

2022年5月19日(木) 14:00 - 15:30

野海 俊文 (神戸大学 大学院理学研究科 物理学専攻 宇宙論研究室 准教授)

In the past years, it has become increasingly clear that there exist nontrivial consistency conditions on symmetries in quantum gravity, that are invisible in classical gravity. The Swampland program aims at identifying such quantum gravity constraints and their implications for particle physics and cosmology, toward quantum gravity phenomenology. In this talk, I will review recent progress in this program, including my own works.

会場: コモンルーム 246-248号室 とZoomのハイブリッド開催

イベント公式言語: 英語

Khovanov homology theory - an introduction to categorification

2022年5月13日(金) 14:00 - 16:30

佐野 岳人 (理化学研究所 数理創造プログラム (iTHEMS) 基礎科学特別研究員)

Jones polynomial is a knot invariant discovered by V. F. R. Jones in 1984. Not only that it is a useful mathematical tool, the discovery led to opening up a new research area, quantum topology, which connects quantum mechanics and low-dimensional topology. In 2000, M. Khovanov introduced a “categorification of the Jones polynomial”, which is now called Khovanov homology, and made categorification one of the fundamental concept in knot theory. Now what does categorification mean, and what is it good for? In this talk, assuming that many of the audience are not familiar with abstract category theory, I will start from easy examples of categories and categorifications, for example categorification of natural numbers, and explain why they are something natural to think of. In the latter part, I will briefly explain the construction of Khovanov homology, and introduce several related topics.

会場: コモンルーム 246-248号室 とZoomのハイブリッド開催

イベント公式言語: 英語

Classical and Quantum Chaos

2022年5月12日(木) 16:00 - 17:00

首藤 啓 (東京都立大学 大学院理学研究科 物理学専攻 教授)

Classical and quantum mechanics in multi-dimensions are qualitatively different from those in one-dimension since they are no more integrable in general and chaos appears in the dynamics. This brings a great deal of complexity or even richness both in classical and quantum dynamics. Especially in generic nonintegrable systems which are neither completely integrable nor fully chaotic, phase space becomes a mixture of regular and chaotic components. Such an aspect is a source of inexhaustible questions not only in the past but in the future. We here overview classical and quantum chaos in Hamiltonian systems.

会場: via Zoom

イベント公式言語: 英語

Introduction to Topological Insulators: Topological Superconductors and Quantum Computing

2022年5月9日(月) 14:00 - 15:30

邱 靖凱 (理化学研究所 数理創造プログラム (iTHEMS) 上級研究員)

会場: via Zoom

イベント公式言語: 英語

Introduction to Topological Insulators: From Quantum to Classical Physics 4

2022年4月27日(水) 15:00 - 17:00

小澤 知己 (東北大学 材料科学高等研究所 (AIMR) 准教授)

In this set of lectures, I give an introduction to topological insulators. A goal is to provide an overall understanding of basic concepts of the physics of topological insulators to mathematicians and physicists with no prior knowledge on the subject. Very roughly speaking, topological insulators are materials whose wavefunctions show nontrivial topological structure in momentum space. Materials with topologically nontrivial wavefunction in momentum space have been found to host modes which are localized at the surface (edge) of the material: a property known as the bulk-edge correspondence. The bulk-edge correspondence results in experimentally observable signature of somewhat abstract notion of topology of the wavefunction in momentum space. Originally, topological insulators were found and studied for electrons in solid-state materials, which are quantum mechanical. However, certain properties of topological insulators, including the bulk-edge correspondence, have been found to hold also for purely classical materials, such as electromagnetic waves obeying Maxwell’s equations, or waves described by Newtonian mechanics. I will try to introduce topological insulators in a way general enough to be applied to quantum as well as classical materials. In the final part of the lectures, I take this opportunity to discuss some of my own works, where I studied some relations between the two-dimensional topological insulators and Kähler geometry.

会場: via Zoom

イベント公式言語: 英語

Introduction to Topological Insulators: From Quantum to Classical Physics 3

2022年4月21日(木) 15:00 - 17:00

小澤 知己 (東北大学 材料科学高等研究所 (AIMR) 准教授)

In this set of lectures, I give an introduction to topological insulators. A goal is to provide an overall understanding of basic concepts of the physics of topological insulators to mathematicians and physicists with no prior knowledge on the subject. Very roughly speaking, topological insulators are materials whose wavefunctions show nontrivial topological structure in momentum space. Materials with topologically nontrivial wavefunction in momentum space have been found to host modes which are localized at the surface (edge) of the material: a property known as the bulk-edge correspondence. The bulk-edge correspondence results in experimentally observable signature of somewhat abstract notion of topology of the wavefunction in momentum space. Originally, topological insulators were found and studied for electrons in solid-state materials, which are quantum mechanical. However, certain properties of topological insulators, including the bulk-edge correspondence, have been found to hold also for purely classical materials, such as electromagnetic waves obeying Maxwell’s equations, or waves described by Newtonian mechanics. I will try to introduce topological insulators in a way general enough to be applied to quantum as well as classical materials. In the final part of the lectures, I take this opportunity to discuss some of my own works, where I studied some relations between the two-dimensional topological insulators and Kähler geometry.

会場: via Zoom

イベント公式言語: 英語