2020年度セミナー
今年度前期は水曜日午後１時３０分からセミナーを行います。 このセミナーの他にも、毎週木曜日１５時から本郷理学部４号館３階１３２０号室にて行われる統計力学セミナーにも参加しています。
| 日程 | 時間 | 講演者 | 演題・要旨 |
| 05月08日(水) Wed, May 8 |
13:30 |
吉田恒也さん（筑波大） Dr. Tsuneya Yoshida (Tsukuba U.) |
Symmetry-protection of non-Hermitian degeneracies for correlated systems 要旨 |
| 05月15日(水) Wed, May 15 |
13:30 |
井戸康太さん（東大物性研） Dr. Kota Ido (ISSP, U. Tokyo) |
Variational Monte Carlo method for electron dynamics 要旨 |
| 05月22日(水) Wed, May 22 |
13:30 |
小澤知己さん（理研） Dr. Tomoki Ozawa (RIKEN) |
Quantum geometric tensor in ultracold gases and other synthetic quantum systems 要旨 |
| 05月29日(水) Wed, May 29 |
13:30 |
山本薫さん（物材機構） Dr. Kaoru Yamamoto (NIMS) |
First-principles calculation of the Seebeck coefficient for Fe/MgO/Fe magnetic tunneling junction 要旨 |
| 06月05日(水) Wed, Jun 05 |
13:30 |
桑原知剛さん（理研） Dr. Tomotaka Kuwahara (RIKEN) |
Approximate quantum Markov network at finite temperatures 要旨 |
| 06月12日(水) Wed, Jun 12 |
13:30 |
川本達郎さん（産総研） Dr. Tatsuro Kawamoto (AIST) |
An algorithmic detectability limit of community detection in graphs 要旨 |
| 06月19日(水) Wed, Jun 19 |
13:30 |
Fabio Bagarello さん（パレルモ大） Dr. Fabio Bagarello (U. Palermo) |
Recent results on non self-adjoint Hamiltonians 要旨 |
第０１回
講師：吉田恒也さん（筑波大）Dr. Tsuneya Yoshida (Tsukuba University)日時：０５月０８日（水）午後１時３０分〜 Wed, May 8, 1:30pm
演題：Symmetry-protection of non-Hermitian degeneracies for correlated systems
要旨：In this decade, topological phases have attracted much interest. As the results of extensive analysis, a variety of topological insulators/superconductors have been reported which arise from interplay between symmetry and the topological properties.
In parallel to the above progress, non-Hermitian systems [1] have been pioneered as new platforms of topological physics [2]. Notably, the platforms of non-Hermitian topological physics extend to a wide range of systems; cold atoms out of equilibrium [2], correlated systems in equilibrium [3,4] etc. As this field has been pioneered very recently, many significant issues remain open questions. One of them is the interplay between symmetry and exceptional points which are topological non-Hermitian degeneracies.
We here address this issue by analyzing correlated systems. Our analysis discovers symmetry-protected non-Hermitian degeneracies [5]. By employing the dynamical mean-field theory, we demonstrate the emergence of symmetry-protected exceptional rings for a honeycomb Hubbard model. If time allows, we also show the emergence of symmetry-protected exceptional rings for classical systems [6], indicating the ubiquity of the symmetry-protected non-Hermitian degeneracies.
参考文献
[1] N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77 570 (1996).
[2] Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Phys. Rev. X 8 031079 (2018).
[3] V. Kozii and L. Fu, arXiv: 1708.05841.
[4] T. Yoshida, R. Peters, and N. Kawakami, Phys. Rev. B 98 035141 (2018).
[5] T. Yoshida, R. Peters, N. Kawakami, and Y. Hatsugai, Phys. Rev. B 99 035141 (2019).
[6] T. Yoshida and Y. Hatsugai, submitted.
第０２回
講師：井戸康太さん（東大物性研）Dr. Kota Ido (ISSP, University of Tokyo)日時：０５月１５日（水）午後１時３０分〜 Wed, May 15, 1:30pm
演題：Variational Monte Carlo method for electron dynamics
要旨：The variational Monte Carlo (VMC) method is a powerful method without the sign problem to perform simulations on quantum many-body systems. This method has been applied to investigate physical properties in a wide range of strongly correlated electron systems. Although most applications of the VMC method were limited to analyses of the ground states, it has been recently shown that the calculations of excited states such as nonequilibrium transient states are possible. In this talk, I present our recent work on the VMC method for correlated electron dynamics and its application to the Hubbard model. I also explain open source software mVMC, which has been recently developed for users to easily perform VMC simulations.
第０３回
講師：小澤知己さん（理研）Dr. Tomoki Ozawa (RIKEN)日時：０５月２２日（水）午後１時３０分〜 Wed, May 22, 1:30pm
演題：Quantum geometric tensor in ultracold gases and other synthetic quantum systems
要旨：Topological and geometrical property of bands have attracted great attention during the past decade due to the development of the study of topological phases of matter in solid-state electron systems. Probably the most well-studied geometrical property of bands is the Berry curvature, integral of which gives rise to the topological Chern number. A less well known geometrical property is the quantum metric, or the Fubini-Study metric, which provides a metric structure in the Brillouin zone. Both Berry curvature and quantum metric are defined through momentum-space derivative of Bloch states, and are both gauge invariant. In fact, we can uniformly describe both concepts in terms of the quantum geometric tensor, real part of which is the quantum metric and imaginary part is the Berry curvature. In this talk, I explain intuitive meaning of the quantum metric, and discuss some physical consequences. I will also discuss recent experimental measurements of the quantum metric in ultracold atomic gases and diamond NV-centers, where the quantum metric was extracted through observation of excitation rates upon periodic modulation to the system.
第０４回
講師：山本薫さん（物材機構）Dr. Kaoru Yamamoto (NIMS)日時：０５月２９日（水）午後１時３０分〜 Wed, May 29, 1:30pm
演題：First-principles calculation of the Seebeck coefficient for Fe/MgO/Fe magnetic tunneling junction
要旨：Recent progress of spin caloritronics enables us to manipulate heat and spin currents. One of the emerging interesting phenomena in spin caloritronics is the analogue of the classical Seebeck effect, such as the magneto-Seebeck effect in magnetic tunneling junctions (MTJs) [1], which is caused by spin-dependent charge current combined with heat current in parallel and anti-parallel magnetization configurations. However, understanding of the magneto-Seebeck effect in MTJs from the property of the material has not been developed so much, although it has been measured and calculated in previous studies [1,2].
In the present work, we calculate the Seebeck coefficients of Fe(7ML)/MgO(nML)/Fe(7ML) MTJ using the first-principles density functional method. The electronic transport coefficients of the MTJs are calculated from the Landauer formula. We find that the interface resonanant tunneling around the Fermi level [3] can enhance the Seebeck effect and that the effect of the resonancant tunneling depends on the in-plane lattice constant of the MTJ and the number of MgO layers [4]. Our results will be important for designing MTJs with high Seebeck coefficient.
参考文献
[1] M. Walter et al., Nat. Mater. 10, 742 (2011).
[2] T. Kuschel et al., J. Phys. D: Appl. Phys. 52, 133001 (2019).
[3] K. D. Belashchenko et al., Phys. Rev. B 72, 140404(R) (2005).
[4] K. Yamamoto, K. Masuda, K. Uchida, and Y. Miura, in preparation.
第０５回
講師：桑原知剛さん（理研）Dr. Tomotaka Kuwahara (RIKEN)日時：０６月０５日（水）午後１時３０分〜 Wed, Jun 05, 1:30pm
演題：Approximate quantum Markov network at finite temperatures
要旨：In recent years, the Gibbs sampling on quantum computer attracts more and more attentions due to the application to exponential quantum speed up of the semidefinite programming problem [1] and the appearance of machine learning using a quantum Boltzmann machine [2]. Here, the quantum Gibbs states are described by e^{-βH}/Z (β: inverse temperature) for the system Hamiltonian H. As methods of quantum Gibbs sampling, Quantum metropolis sampling algorithm [3] and Davies Gibbs sampling algorithm [4] have been well-known. These algorithms heuristically works well, but the precision analyses are generally extremely difficult and the convergence is often exponentially slower with respect to the system size (eg, spin glass system). Our motivation in this research is to clarify under what conditions the quantum Gibbs sampling is implemented efficiently.
For the purpose, we will first introduce a method to utilize the quantum Markov property. When the system is decomposed into A, B, and C subsystems, we call that a quantum state is approximately Markov if the conditional mutual information I(A,C|B) between A and C via B exponentially decays with respect to the distance between A and C. If the Gibbs state is given by the approximate Markov network, we know that the quantum sampling can be efficiently implemented by a small depth local quantum circuits [5].
In this talk, I will show that such a quantum Markov property always hold for quantum Gibbs states above a certain threshold temperature. In addition to the efficient quantum Gibbs sampling, I will also explain several implications of the quantum Markov property: the strong versions of the area law, the clustering theorem, and existence of the topological entanglement entropy. This is a joint work with Kohtaro Kato and Fernando Brandão in Caltech IQIM.
参考文献
[1] F. G. S. L. Brandão and K. M. Svore, IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), pp. 415 (2017).
[2] M. H. Amin, et al., Phys. Rev. X 8, 021050 (2018).
[3] K. Temme, T. J. Osborne, K. G. Vollbrecht, D. Poulin, and F. Verstraete, Nature 471, 87 (2011).
[4] M. J. Kastoryano and F. G. S. L. Brandão, Commun. Math. Phys., 344, 915 (2016).
[5] F. G. S. L. Brandão and M. J. Kastoryano, Commun. Math. Phys., 365, 1 (2019).
第０６回
講師：川本達郎さん（産総研）Dr. Tatsuro Kawamoto (AIST)日時：０６月１２日（水）午後１時３０分〜 Wed, Jun 12, 1:30pm
演題：An algorithmic detectability limit of community detection in graphs
要旨：Modularity maximization [1] using greedy algorithms continues to be a popular approach toward community detection in graphs, even after various better forming algorithms have been proposed. Apart from its clear mechanism and ease of implementation, this approach is persistently popular because, presumably, its risk of algorithmic failure is not well understood. In this talk [2], we provide an insight into this issue by estimating the algorithmic performance limit of the stochastic block model inference using modularity maximization. This is achieved by counting the number of metastable states under a local update rule [3]. Our results offer a quantitative insight into the level of sparsity at which a greedy algorithm typically fails.
参考文献
[1] M. E. J. Newman and M. Girvan, Phys. Rev. E 69, 026113 (2004).
[2] T. Kawamoto and Y. Kabashima, Phys. Rev. E 99, 010301(R) (2019).
[3] F. Tanaka and S. F. Edwards, J. Phys. F: Metall. Phys. 10, 2769 (1980).
第０７回
講師：Fabio Bagarello さん（パレルモ大）Dr. Fabio Bagarello (U. Palermo)日時：０６月１９日（水）午後１時３０分〜 Wed, Jun 19, 1:30pm
演題：Recent results on non self-adjoint Hamiltonians
要旨：We discuss some recent results on quantum systems whose dynamics is driven by certain non self-adjoint Hamiltonians. In particular, after a short introduction on modified commutation and anti-commutation relations, our plan is to discuss a finite-dimensional version of the CCR, a possible deformed version of the so-called generalized Heisenberg algebra, and a no-go result for the damped quantum harmonic oscillator. We also will discuss some results on tridiagonal non self-adjoint factorizable Hamiltonians, and on their SUSY counterparts.
第０１回 No. 01
講師 Speaker: 平良敬信さん（東京大）Dr. Takanobu Taira (IIS, The University of Tokyo)日時 Date: １０月１９日（水）午後２時〜 Wed, Oct 19, 2:00pm
演題 Title: The breakdown of the Higgs mechanism at the exceptional point
要旨 Abstract: The non-Hermitian physics has seen intensive theoretical and experimental development over the past decades. One of the key features of the non-Hermitian system is the branch point of the eigenvalue called the exceptional point, where the rank of the non-Hermitian operator is reduced. We will briefly review PT-symmetric quantum mechanics and present a non-Hermitian extension of the Yang-Mills theory coupled with Higgs fields. We will show that the classical mass of massive gauge and t'Hooft-Polyakov monopole vanishes at the exceptional point while the vacuum solution stays finite.
第０２回 No. 02
講師 Speaker: 多賀圭理さん（早大） Mr. Keisuke Taga (Waseda U.)日時 Date: １０月２６日（水）午後２時１５分〜 Wed, Oct. 26, 2:15pm
演題 Title: Koopman operator analysis for the elementary cellular automata
要旨 Abstract: The Koopman operator theory for analyzing nonlinear dynamical systems has attracted much attention recently. The Koopman operator is a linear operator which gives the time evolution of the observables of the dynamical system, thus, we can analyze nonlinear systems by using the methods for linear systems. On the other hand, because the Koopman operator acts on a function space of observables, it can be generally infinite-dimensional and difficult to analyze. In this talk, I will introduce the Koopman operator for the finite state system. In this case, the Koopman operator is finite-dimensional, and we can derive a finite-dimensional representation of the Koopman operator and construct the Koopman eigenvalues and Koopman eigenfunctions explicitly. I will show that the Koopman analysis of finite state systems can reveal fundamental properties of the system, such as reversibility and conserved quantities. I will also introduce dynamic mode decomposition (DMD), a data-driven method to obtain an approximation of the Koopman operator from time-series data, for the finite state system. The theoretical results will be applied to elementary cellular automata, which have been studied as models of real-world systems, such as pigmentation patterns on shells, peeling patterns of adhesive tapes, and congestion dynamics of traffic flow as examples of the simplest system exhibiting spatiotemporal dynamics.
第０３回 No. 03
講師 Speaker: Dr. Thierry Martin (U. Aix-Marseille)日時 Date: １１月２日（水）午後１時〜 Wed, Nov. 2, 1:00pm
演題 Title: Quantum transport in conventional and topological superconducting hybrid systems
要旨 Abstract: In nano-physics, an electron can be transferred into the gap of a superconductor provided that it is accompanied by another electron in order to form Cooper pairs. I will review a few phenomena where this Andreev reflection processes play a role and examine how transport through topological superconductors can be illustrated to test the relevance of Majorana fermions.
第０４回 No. 04
講師 Speaker: 望月健さん（理研）Dr. Ken Mochizuki (RIKEN)日時 Date: １１月９日（水）午後２時３０分〜 Wed, Nov. 9, 2:30pm
演題 Title: Complexity transitions in non-unitary boson sampling dynamics
要旨 Abstract: Non-Hermitian quantum mechanics have been extensively studied as an effective theory for open quantum systems exhibiting non-unitary dynamics, and various intriguing phenomena have been revealed. Non-Hermitian dynamics has been observed not only in genuinely quantum systems but also in classical systems. In that sense, it is a fundamental but largely unexplored question to what extent non-He rmitian quantum mechanics exhibits unique quantum nature distinct from classic al systems. In isolated quantum systems, unique quantum nature can be discusse d by its computational complexity. It is investigated in the boson sampling problem, where probability distributions of bosons can be hard to sample by classical computers.
In the seminar, I report novel transitions concerning the computational complexity in non-unitary dynamics of bosons. We find that PT-symmetry breaking, which is a unique phenomenon in non-Hermitian open quantum systems, is profoundly related to the computational complexity of the boson sampling problem. In the PT -broken phase, there is a dynamical transition where the probability distribution of bosons becomes approximated by that of distinguishable particles, which leads to the easiness of the boson sampling with classical computers. Thus, PT symmetry breaking makes bosonic systems enter classical regime. We discuss that the enhancement of the classical nature in terms of the easiness for sampling is ensure d in the long-time regime in a wide range of non-unitary boson sampling dynamics.
参考文献 References
Ken Mochizuki and Ryusuke Hamazaki, arXiv:2207.12624
第０５回 No. 05
講師 Speaker: 羽田野直道 Naomichi Hatano日時 Date: １１月１６日（水）午後１時〜 Wed, Nov. 16, 1:00pm
演題 Title: Arrow of time in quantum mechanics
要旨 Abstract: Why does the time flow only in one particular direction? This is a very big and fundamental question of physics, called the problem of "the arrow of time." There are a few types of the arrow of time. The cosmological arrow of time refers to the direction of time in our universe as we see it. The psychological arrow of time refers to the direction of time that we perceive.
The arrow of time that I am going to discuss in the present talk is the dynamical arrow of time, which refers to the following problem. The fundamental equations of motion, namely the Newton equation for classical mechanics and the Schroedinger equation for quantum mechanics, are symmetric if we flip the arrow of time. Nonetheless, we see the oscillation of a pendulum always diminishes and an excited state always decays into the ground state. How can this inconsistency arise? There have been many answers to it but most of them attribute the reason to the limitation of our ability of measuring physical systems. My collaborator Gonzalo Ordonez and I have reservations because it almost sounds like the dynamical arrow of time could be flipped or eliminated if we have more abilities!
We answer the question of the dynamical arrow of time in the realm of quantum mechanics in the following way. We succeeded in deriving a time-reversal symmetric decomposition of the time evolution operator which contains both decaying states and growing states symmetrically. If we watch the time evolution starting from an initial condition, we pick all the decaying states, whereas if we watch the time evolution ending in a terminal condition, we pick all the growing states. This shows that the arrow of time is generated by the difference in the way we watch the time evolution.
References:
- G. Ordonez, N. Hatano, The arrow of time in open quantum systems and dynamical breaking of the resonance-anti-resonance symmetry, J. Phys. A: Math. Theor. 50 (2017) 405304 (34pp)
- G. Ordonez, N. Hatano, Irreversibility and the breaking of resonance-antiresonance symmetry, Chaos 27 (2017) 104608 (10pp)
- N. Hatano and G. Ordonez, Time-Reversal Symmetry and Arrow of Time in Quantum Mechanics of Open Systems, Entropy 21 (2019) 380 (14 pages)
第０６回 No. 06
講師 Speaker: 曽根和樹さん（東大）Mr. Kazuki Sone (U. Tokyo)日時 Date: １２月１４日（水）午後２時３０分〜 Wed, Oct. 9, 2:30pm
演題 Title: To be announced.
要旨 Abstract: To be announced.