統計力学セミナー予定表 2017年度


連絡先: 島田尚(shimadaあっと ap.t.u-tokyo.ac.jp)、 森貴司(moriあっと spin.phys.s.u-tokyo.ac.jp)
宮下研究室伊藤研究室 (セミナー)| 藤堂研究室羽田野研究室 (セミナー)| 桂研究室

これからのセミナー

日時 場所 講演者(敬称略) 講演題目
6月19日13時 理学部4号館 1320教室 赤城 裕 Noncommutative Z2 index of 3D topological insulators with disorder
6月26日13時 理学部4号館 1320教室 宮下 精二 TBA
7月3日13時 理学部4号館 1320教室 森 貴司 TBA
7月10日13時 理学部4号館 1320教室 檜原 太一 TBA

これまでのセミナー

日時 講演者(敬称略) 講演題目
4月17日13時 Ramis Movassagh (MIT, US) Eigenvalue Attraction
4月24日13時 大久保 毅 Ground state properties of Na2IrO3 determined from ab initio Hamiltonian
5月8日13時 桂 法称 Quantum Hangul
5月15日13時 Kay Brandner (Aalto University, Finland) Experimental Determination of Dynamical Lee-Yang Zeros
5月22日13時 伊藤 伸泰 Data-transfer optimization of quantum simulation on massive parallel computers
5月29日13時 藤堂 眞治 Crystal Structure Prediction Supported by Incomplete Experimental Data
6月5日13時 羽田野 直道 Does non-Hermiticity weaken localization?
6月12日13時 鈴木 貴文 (東大物工, 今田研) Nonequilibrium Kondo Resonance from Viewpoints of Electron Quantum Optics
所属が書かれていない講演者は、宮下研、伊藤研、藤堂研、羽田野研、桂研の所属です。
過去のセミナー: 2016年度| 2015年度2015年度2014年度2013年度2012年度2011年度2010年度2009年度2008年度2007年度2006年度2005年度2004年度2003年度2002年度2001年度2000年度1999年度

第1回

日時: 4月17日13時より

場所: 1320教室

講演者: Ramis Movassagh (MIT, US)

講演タイトル:Eigenvalue Attraction

講演要旨:
Much work has been developed to the understanding of the motion of eigenvalues in response to randomness. The folklore of randam matrix analysis, especially in the case of Hermitian matrices, suggests that the eigenvalues of a perturbed matrix repel. We prove that the complex conjugate (c.c.) eigenvalues of a smoothly varying real matrix attract. We offer a dynamical perspective on the motion and interaction of the eigenvalues in the complex plane, derive their governing equations and discuss applications. C.c. pairs closest to the real axis, or those that are ill-conditioned, attract most strongly and can collide to become exactly real. We apply the results to the Hatano-Nelson model, random perturbations of a fixed matrix, real stochastic processes with zero-mean and independent intervals and discuss open problems. Time permitting we will discuss a joint work with Leo Kadanoff, on Toeplitz matrices with singular Fisher-Hartwig symbols.

Reference: J. Stat. Phys. 162, 615 (2016).

第2回

日時: 4月24日13時より

場所: 1320教室

講演者: 大久保 毅

講演タイトル:Ground state properties of Na2IrO3 determined from ab initio Hamiltonian

講演要旨:
Novel quantum phenomena induced by strong spin-orbit interaction have recently attracted much interest in condensed matter physics. Iridium oxides offer a typical example that shows rich phenomena. Among them, A2IrO3 (A=Na or Li) have intensively been investigated since the theoretical proposal that the Kitaev spin liquid would be realized [1, 2].

In this seminar, we discuss the ground state properties of Na2IrO3 based on the ab initio Hamiltonian represented by Kitaev and extended Heisenberg interactions [3]. By means of the infinite-size PEPS tensor network method, the two-dimensional density matrix renormalization group, and the exact diagonalization we show that the ground state of Na2IrO3 is a magnetically ordered state with zigzag configuration in agreement with experimental observations [4]. We also discuss the phase diagram in the parameter space away from the ab initio value of Na2IrO3 controlled by the trigonal distortion. It turns out that the phase diagram contains several magnetically ordered phases near the zigzag phase [4]. It suggests that potentially rich magnetic structures may appear in A2IrO3 compounds for A other than Na.

[1]. G. Jackeli, and G. Khaliullin, Phys. Rev. Lett. 102, 017205 (2009).
[2]. J. Chaloupka, G. Jackeli, and G. Khaliullin, Phys. Rev. Lett. 105, 027204 (2010).
[3]. Y. Yamaji, Y. Nomura, M. Kurita, R. Arita, and M. Imada, Phys. Rev. Lett. 113, 107201 (2014).
[4]. T. Okubo, K. Shinjo, Y. Yamaji, N. Kawashima, S. Sota, T. Tohyama, M. Imada, arXiv:1611.03614.

第3回

日時: 5月8日13時より

場所: 1320教室

講演者: 桂 法称

講演タイトル:Quantum Hangul

講演要旨:
Resonating valence bond (RVB) states proposed by Anderson have been the focus of much attention because of their relevance to the physics of spin liquids. However, previous work was overwhelmingly dominated by RVB states built out of dimers, each of which is made up of two S=1/2 spins. As an alternative route to spin liquids, we propose RVB states consisting of trimer motifs. Here by trimer we mean the spin singlet made up of three S=1 spins. The trimer RVB (tRVB) state is an equal-weight superposition of all possible trimer arrangements. The problem of counting trimer coverings is, in itself, a fascinating combinatorial problem. In the talk, we introduce a quantum trimer model on a square lattice for which the tRVB state becomes the exact ground state. The state is shown to be 9-fold degenerate on a torus. We also show that the correlation functions in the ground state are extremely short-ranged, suggesting that the model is gapped and exhibits Z_3 topological order.

Reference:
[1] H. Lee, Y-T. Oh, J.H. Han, and H. Katsura, Phys. Rev. B, 95, 060413(R) (2017).

第4回

日時: 5月15日13時より

場所: 1320教室

講演者: Kar Brandner (Aalt University, Finland)

講演タイトル:Experimental Determination of Dynamical Lee-Yang Zeros

講演要旨:
Conventional phase transitions involve abrupt changes of a macroscopic system in response to small variations of an external control parameter. This exceptional behaviour can be understood from the complex zeros of the partition function of the finite-sized system: in the thermodynamic limit, these Lee-Yang zeros, which correspond to logarithmic singularities of the free energy, approach the critical value of the control parameter on the real axis.

This general scheme also applies to dynamical phase transitions in non-equilibrium systems. The partition function is thereby replaced with the moment-generating function of a stochastic process with the counting field playing the role of the external control parameter. Here, we demonstrate that the corresponding dynamical Lee-Yang zeors are not only a theoretical conecept but physical observables, which encode remarkable information on the long-time statistics and the dynamical fluctuations of the system. To this end, we analyze a stochastic process involving Andreev-tunneling events in a mesososcopic device consisting of a normal-state island and two superconducting leads. From measurements of the dynamical activity, we extract the Lee-Yang zeros, which reveal a smeared dynamical phase transition outside the range of direct observations. Being obtaind only from short-time data, this information allows us to predict the large-deviation statistics of the dynamical activity at long times, which is otherwise difficult to measure. Our method paves the way for further experiments on the statistical mechanics of many-body systems out of equilibrium.

Reference: K. Brandner, V. F. Maisi, J. P. Pekola, J. P. Garrahan, C. Flindt, "Experimental Determination of Dynamical Lee-Yang Zeros", Phys. Rev. Lett. 118, 180601 (2017).

第5回

日時: 5月22日13時より

場所: 1320教室

講演者: 伊藤 伸泰

講演タイトル: Data-transfer optimization of quantum simulation on massive parallel computers

講演要旨:
Brute force simulations using full vectors in Hilbert spaces requre exponentially large memory spaces versus degree-of-freedom. Memory space and its band-width of modern massive-parallel supercomputers are useful for the purpose, but internode datat-ransfer is order-of-magnitude more expensive than intranode operations, so optimization of data-transfer is important for such simulation. A heuristic algorithm for the world-record simulation of qbit simulation will be discussed as an example.

第6回

日時: 5月29日13時より

場所: 1320教室

講演者: 藤堂 眞治

講演タイトル: Crystal Structure Prediction Supported by Incomplete Experimental Data

講演要旨:
The prediction of crystal structure from chemical composition has been a long-standing challenge in natural science. Although various numerical methods have been developed over last decades, it i remains still difficult to numerically predict crystal structures comprising more than several tens of atoms in the supercell due to the many degrees of freedom, which increase exponentially with the number of atoms. Here, we propose a new method for crystal structure prediction from numerical simulations with support of X-ray diffraction experimental data [1]. We show that even if the experimental data is totally insufficient for conventional structure analysis, it can still support and substantially accelerate structure simulation. In particular, we formulate a cost function based on a weighted sum of interatomic potential energy and a penalty function referred to as "crystallinity", which is defined by using limited X-ray diffraction data. We present the simulation results for well-known polymorphs of SiO2 with up to 96 atoms in the supercell, in which the correct structures can be reproduced with high probability with a very limited number of diffraction peaks. We also present an optimization method for simultaneous minimization of two or more cost functions which share the same global minimum point, but have different distributions of local minima. We discuss the possibility that our new optimization method can further accelerate the convergence to the global minimum in the crystal structure simulation [2].

[1] N. Tsujimoto, D. Adachi, R. Akashi, S. Todo, S. Tsuneyuki, arXiv:1705.08613.
[2] D. Adachi, N. Tsujimoto, R. Akashi, S. Todo, S. Tsuneyuki, in preparation.

第7回

日時: 6月5日13時より

場所: 1320教室

講演者: 羽田野 直道

講演タイトル: Does non-Hermiticity weaken localization?

講演要旨:
The Anderson localization refers to a phenomenon of spatial localization of waves in random media. It is often explained to be originated in coherence; the destructive interference among the incident wave and all randomly scattered waves makes the wave stay in a region where the randomness happens to be strong. Many people therefore have suggested that one can weaken the wave localization by undermining the wave coherence.

One important way of possibly eroding the coherence is to introduce the non-Hermiticity. Indeed, we have shown that the off-diagonal non-Hermiticity destroys the localization even in one spatial dimension [1-4], where the Anderson localization takes place most strongly. Several other studies also suggested that complex potentials on the diagonal randomness weakens the Anderson localization.

Does the non-Hermiticity universally weaken the Anderson localization by impairing the coherence? Is there a counter-example? I will discuss this issue utilizing our recent algorithm of computing the localization length of non-Hermitian random systems [5].

Collaborators: Amnon Aharony (Tel Aviv University & Ben-Gurion University of the Negev); Joshua Feinberg (University of Haifa)

References
[1] N. Hatano and D.R. Nelson, Phys. Rev. Lett. 77, 570―573 (1996)
[2] N. Hatano and D.R. Nelson, Phys. Rev. B 56, 8651―8673 (1997)
[3] N. Hatano, Physica A 254, 317―331 (1998)
[4] A. Amir, N. Hatano and D.R. Nelson, Phys. Rev. E 93, 042310 (2016)
[5] N. Hatano and J. Feinberg, Phys. Rev. E 94, 063305 (2016)

第8回

日時: 6月12日13時より

場所: 1320教室

講演者: 鈴木 貴文 (東大物工, 今田研)

講演タイトル: Nonequilibrium Kondo Resonance from Viewpoints of Electron Quantum Optics

講演要旨:
The Kondo effect has attracted renewed attention in the condensed matter physics because of rapid development in nanotechnologies. In particular, a quantum dot (QD) system enables us to study the nonequilibrium Kondo effect with experimentally tuned parameters. The interplay between the coherent many-body resonance and the nonequilibrium field has posed fundamental problems of determining the elementary excitation in the Kondo systems driven out of equilibrium [1,2].

Recently, it was experimentally demonstrated that Lorentzian-shaped periodic pulses can create an ideal fermionic excitation above the Fermi sea [3]. The quasiparticle was named "leviton" after Leonid S. Levitov, who theoretically predicted the nontrivial property of the Lorentzian pulse over twenty years ago [4]. The experimental realization of the on-demand single-electron generator has made significant contributions to advancing the emerging field of electron quantum optics.

In this talk, we discuss the coherent transport of levitons through the QD system in the Kondo regime [5]. The Kondo resonance repeatedly emerges in the nonequilibrium regimes where the Fermi sea is driven by optimal Lorentzian pulses without particle-hole excitations.

[1] A. Oguri, J. Phys. Soc. Jpn. 74, 110 (2005).
[2] M. Ferrier et al., Nat. Phys. 12, 230 (2016)
[3] J. Dubois et al., Nature (London) 502, 659 (2013)
[4] L. S. Levitov et al., J. Math. Phys. 37, 4845 (1996).
[5] T. J. Suzuki, arXiv:1703.05198 (to be published in PRB)

第9回

日時: 6月19日13時より

場所: 1320教室

講演者: 赤城 裕

講演タイトル: Noncommutative Z2 index of 3D topological insulators with disorder

講演要旨:
Topological insulators in three dimensions characterized by a Z2 topological invariant have attracted much attention due to their gapless surface states robust against perturbations. In translationally invariant systems, the Z2 invariant is defined in terms of Bloch wave functions [1]. However, it is not obvious how to define such an invariant in disordered systems, where the Bloch momentum is no longer a good quantum number.

Recently, it was found that the methods of noncommutative geometry [2] provide a mathematically rigorous representation of the Z2 invariant [3,4], which is particularly useful for studying systems without translational symmetry. We take the Wilson-Dirac-type Hamiltonian as an example and demonstrate how the noncommutative formula allows us to map out the phase diagram numerically. Our results [5] are consistent with those obtained by a transfer-matrix method in previous work [6]. In this presentation, I will explain how to define the noncommutative Z2 index, and numerically demonstrate its robustness against disorder.

[1] L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 98, 106803 (2007).
[2] J. E. Avron, R. Seiler, and B. Simon, J. Func. Anal. 120, 220 (1994).
[3] H. Katsura and T. Koma, J. Math. Phys. 57, 021903 (2016).
[4] H. Katsura and T. Koma, Preprint, arXiv:1611.01928.
[5] Y. Akagi, H. Katsura, and T. Koma, in preparation.
[6] K. Kobayashi, T. Ohtsuki, and K. Imura, Phys. Rev. Lett. 110, 236803 (2013).