乱れや相互作用のある系のトポロジカル相とその不変量

• Project Area: Discrete Geometric Analysis for Materials Design
• Project/Area Number: 18H04478
• Research Category: Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)
• Allocation Type: Single-year Grants
• Research Institution: The University of Tokyo
• Principal Investigator: 桂 法称 東京大学, 大学院理学系研究科(理学部), 准教授 (80534594)
• Project Period (FY): 2018-04-01 – 2020-03-31
• Project Status: Completed (Fiscal Year 2019)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2019: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000); Fiscal Year 2018: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
• Keywords: トポロジカル相 / トポロジカル不変量 / マグノン / SPT相 / マヨラナ・フェルミオン / 機械学習 / Kitaev模型

Outline of Annual Research Achievements

当該年度の主な成果として、以下の２つに関するものが挙げられる。（１）マグノンのトポロジカル相とZ2トポロジカル不変量、（２）遍歴ボゾン系における対称性に守られたトポロジカル相。

（１）磁性体中の素励起であるマグノンのトポロジカル相について、昨年度から継続して研究を行った。特に、昨年度、電子系におけるスピンホール効果のマグノン系における対応物について考察し、この系がZ2トポロジカル不変量によって特徴づけられることを見出した。マグノンのようなボゾン系においてこの不変量を定義するには、擬時間反転対称性と呼ばれる対称性が重要となるが、当該年度は、このような対称性をもつ系の３次元への拡張を試みた。その結果、マグノン系についても電子系と同様に、相を特徴づける４つのZ2不変量の組を定義することが可能であることを明らかにした。この不変量に応じて、(i) 強いトポロジカル相、(ii)弱いトポロジカル相、(iii)自明相の３つの異なる相が現れるが、特に(i)ではギャップレスの表面状態が（奇数個）現れる。また、この表面状態の物理的帰結として、表面に磁場を印加することにより引き起こされる熱ホール効果についても議論した。
（２）スピン自由度をもつ遍歴ボゾン系の対称性に守られたトポロジカル(SPT)相についての研究を行った。特に、デルタ鎖と呼ばれる、平坦なバンドをもつ格子上のF=1 Bose-Hubbard模型において、SPT相の典型例であるHaldane相が存在することを、解析的・数値的手法を総合的に用いて示した。特に、特殊なパラメターについては、基底状態が遍歴系でありながら行列積状態で書き下せることを明らかにした。この基底状態の波動関数の構造は、他の格子や２次元以上への拡張も可能であり、今後の進展も期待される。

その他にも、散逸のある量子多体系のマヨラナ・フェルミオンを用いた解析などの研究を行った。

Research Progress Status

令和元年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和元年度が最終年度であるため、記入しない。

Research Products

• [Int'l Joint Research] ダブリン高等研究所(アイルランド)
• [Int'l Joint Research] Utrecht University(オランダ)
• [Journal Article] Simulating quantum circuits by adiabatic computation: Improved spectral gap bounds (2020)
  • Author(s): Dooley Shane、Kells Graham、Katsura Hosho、Dorlas Tony C.
  • Journal Title: Physical Review A Volume: 101 Issue: 4
  • DOI: 10.1103/physreva.101.042302
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Onsager’s Scars in Disordered Spin Chains (2020)
  • Author(s): Shibata Naoyuki、Yoshioka Nobuyuki、Katsura Hosho
  • Journal Title: Physical Review Letters Volume: 124 Issue: 18 Pages: 180604-180604
  • DOI: 10.1103/physrevlett.124.180604
  • Peer Reviewed
• [Journal Article] Dissipative spin chain as a non-Hermitian Kitaev ladder (2019)
  • Author(s): Shibata Naoyuki、Katsura Hosho
  • Journal Title: Physical Review B Volume: 99 Issue: 17
  • DOI: 10.1103/physrevb.99.174303
  • Peer Reviewed
• [Journal Article] Dissipative quantum Ising chain as a non-Hermitian Ashkin-Teller model (2019)
  • Author(s): Shibata Naoyuki、Katsura Hosho
  • Journal Title: Physical Review B Volume: 99 Issue: 22
  • DOI: 10.1103/physrevb.99.224432
  • NAID: 130008152905
  • Peer Reviewed
• [Journal Article] Three-dimensional topological magnon systems (2019)
  • Author(s): Kondo Hiroki、Akagi Yutaka、Katsura Hosho
  • Journal Title: Physical Review B Volume: 100 Issue: 14
  • DOI: 10.1103/physrevb.100.144401
  • Peer Reviewed
• [Journal Article] Ferromagnetism in the SU(n) Hubbard model with a nearly flat band (2019)
  • Author(s): Tamura Kensuke、Katsura Hosho
  • Journal Title: Physical Review B Volume: 100 Issue: 21
  • DOI: 10.1103/physrevb.100.214423
  • Peer Reviewed
• [Journal Article] ニューラルネットワークによる物理状態の判定から表現まで (2019)
  • Author(s): 吉岡信行、赤城 裕、桂 法
  • Journal Title: 固体物理 Volume: 54 Pages: 51-65
  • NAID: 40022024599
• [Journal Article] Z(2) topological invariant for magnon spin Hall systems (2019)
  • Author(s): Kondo Hiroki, Akagi Yutaka, Katsura Hosho
  • Journal Title: PHYSICAL REVIEW B RAPID COMMUNICATIONS Volume: 99 Issue: 4
  • DOI: 10.1103/physrevb.99.041110
  • NAID: 130007736905
  • Peer Reviewed
• [Journal Article] Rigorous Results for the Ground States of the Spin-2 Bose-Hubbard Model (2019)
  • Author(s): Yang Hong、Katsura Hosho
  • Journal Title: Physical Review Letters Volume: 122 Issue: 5
  • DOI: 10.1103/physrevlett.122.053401
  • NAID: 130007736183
  • Peer Reviewed
• [Journal Article] Supersymmetry breaking and Nambu-Goldstone fermions in interacting Majorana chains (2019)
  • Author(s): Sannomiya Noriaki、Katsura Hosho
  • Journal Title: Physical Review D Volume: 99 Issue: 4 Pages: 045002-045002
  • DOI: 10.1103/physrevd.99.045002
  • Peer Reviewed
• [Journal Article] Transforming generalized Ising models into Boltzmann machines (2019)
  • Author(s): Yoshioka Nobuyuki、Akagi Yutaka、Katsura Hosho
  • Journal Title: Physical Review E Volume: 99 Issue: 3 Pages: 032113-032124
  • DOI: 10.1103/physreve.99.032113
  • Peer Reviewed
• [Journal Article] Learning disordered topological phases by statistical recovery of symmetry (2018)
  • Author(s): Yoshioka Nobuyuki, Akagi Yutaka, Katsura Hosho
  • Journal Title: PHYSICAL REVIEW B Volume: 97 Issue: 20 Pages: 205110-205118
  • DOI: 10.1103/physrevb.97.205110
  • Peer Reviewed
• [Journal Article] Parity-time-symmetric topological superconductor (2018)
  • Author(s): Kawabata Kohei、Ashida Yuto、Katsura Hosho、Ueda Masahito
  • Journal Title: Physical Review B Volume: 98 Issue: 8 Pages: 085116-085116
  • DOI: 10.1103/physrevb.98.085116
  • Peer Reviewed
• [Journal Article] Exact ground states for interacting Kitaev chains (2018)
  • Author(s): Wouters Jurriaan、Katsura Hosho、Schuricht Dirk
  • Journal Title: Physical Review B Volume: 98 Issue: 15
  • DOI: 10.1103/physrevb.98.155119
  • Peer Reviewed
• [Journal Article] Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models (2018)
  • Author(s): Iyoda Eiki、Katsura Hosho、Sagawa Takahiro
  • Journal Title: Physical Review D Volume: 98 Issue: 8 Pages: 086020-086020
  • DOI: 10.1103/physrevd.98.086020
  • Peer Reviewed / Open Access
• [Presentation] Three-dimensional topological magnon systems (2020)
  • Author(s): Hiroki Kondo
  • Organizer: APS March Meeting 2020, online
  • Int'l Joint Research
• [Presentation] Haldane Phase in Spin-1 Bose-Hubbard Model with Flat Band (2020)
  • Author(s): Hong Yang
  • Organizer: APS March Meeting 2020, online
  • Int'l Joint Research
• [Presentation] Dissipative quantum Ising chain as a non-Hermitian Ashkin-Teller model (2020)
  • Author(s): Naoyuki Shibata
  • Organizer: APS March Meeting 2020, online
  • Int'l Joint Research
• [Presentation] スピン自由度をもつBose-Hubbard模型のSPT相 (2020)
  • Author(s): 桂法称
  • Organizer: トポロジカル表面状態、ソリトンとブレーン、指数定理, 大阪大学, 大阪
• [Presentation] 時間反転×並進対称性に保護されたマグノンディラック表面状態と電場応答 (2020)
  • Author(s): 近藤寛記, 赤城裕, 桂法称
  • Organizer: 日本物理学会 第75回年次大会, 2020年３月, 名古屋大学（中止のため、講演概要提出による発表）
• [Presentation] Topological invariants and surface states in magnon systems (2019)
  • Author(s): Hiroki Kondo
  • Organizer: Topological phase workshop, Sendai
  • Int'l Joint Research
• [Presentation] Integrable dissipative spin chains (2019)
  • Author(s): Naoyuki Shibata
  • Organizer: IIS-Chiba Workshop NH2019, Kashiwa
  • Int'l Joint Research
• [Presentation] Rigorous Results on the Ground States of the Spin-2 Bose-Hubbard Model (2019)
  • Author(s): Hong Yang and Hosho Katsura
  • Organizer: The Fourth Kyoto-Beijing-Tokyo Workshop on Ultracold Atomic Gases, YITP, Kyoto
  • Int'l Joint Research
• [Presentation] Integrable dissipative spin chains (2019)
  • Author(s): Naoyuki Shibata and Hosho Katsura
  • Organizer: Thermalization, Many body localization and Hydrodynamics, ICTS, Bangalore
  • Int'l Joint Research
• [Presentation] Rigorous Results on the Ground States of the Spin-2 Bose-Hubbard Model (2019)
  • Author(s): Hong Yang and Hosho Katsura
  • Organizer: Thermalization, Many body localization and Hydrodynamics, ICTS, Bangalore
  • Int'l Joint Research
• [Presentation] Three-dimensional topological magnon systems (2019)
  • Author(s): Hiroki Kondo
  • Organizer: International Conference on Topological Materials Science 2019 (TopoMat2019), Kyoto
  • Int'l Joint Research
• [Presentation] Frustration-free Majorana fermion models (2019)
  • Author(s): Hosho Katsura
  • Organizer: Interacting Majorana Fermions, University of Britich Columbia, Vancouver
  • Int'l Joint Research / Invited
• [Presentation] Supersymmetry breaking and Nambu-Goldstone fermions in lattice models (2019)
  • Author(s): Hosho Katsura
  • Organizer: KIAS Workshop on Topology and Correlation in Quantum Materials, Busan
  • Int'l Joint Research / Invited
• [Presentation] Integrable dissipative spin chains (2019)
  • Author(s): Hosho Katsura
  • Organizer: Amsterdam Summer Workshop on Low-D Quantum Condensed Matter 2019, Amsterdam
  • Int'l Joint Research / Invited
• [Presentation] Integrable dissipative spin chains (2019)
  • Author(s): Hosho Katsura
  • Organizer: Topological phase workshop, Sendai
  • Int'l Joint Research / Invited
• [Presentation] 散逸のある量子 Ising 鎖と非エルミート Ashkin-Teller 模型 (2019)
  • Author(s): 柴田直行, 桂法称
  • Organizer: 日本物理学会2019年秋季大会, 岐阜大学, 岐阜
• [Presentation] The Haldane Phase of Spinful Bosons with Flat Band (2019)
  • Author(s): Hong Yang, 桂法称
  • Organizer: 日本物理学会2019年秋季大会, 岐阜大学, 岐阜
• [Presentation] 量子開放系の問題へのマヨラナ・フェルミオンの応用 (2019)
  • Author(s): 桂法称
  • Organizer: 第12回トポロジー連携研究会「マヨラナ励起の実証に向けて」, 東京工業大学, 東京
  • Int'l Joint Research
• [Presentation] Z2 topological invariant for magnon spin Hall systems (2019)
  • Author(s): Hiroki Kondo
  • Organizer: Topological Phases and Functionality of Correlated Electron Systems 2019 (TPFC2019)
  • Int'l Joint Research
• [Presentation] Z2 topological invariant for magnon spin Hall systems (2019)
  • Author(s): Hiroki Kondo
  • Organizer: APS March Meeting 2019
  • Int'l Joint Research
• [Presentation] Z2 invariants for disordered topological insulators and superconductors (2019)
  • Author(s): Hosho Katsura
  • Organizer: Theoretical studies of topological phases of matter
  • Int'l Joint Research / Invited
• [Presentation] ３次元Z2トポロジカルマグノン系とその表面ディラック状態 (2019)
  • Author(s): 近藤寛記
  • Organizer: 日本物理学会 第74回年次大会
• [Presentation] 縮退した基底状態をもつ非一様なXXZスピン鎖 (2019)
  • Author(s): 桂法称
  • Organizer: 日本物理学会 第74回年次大会
• [Presentation] Z2 Topological Invariant for Magnon Spin Hall Systems (2018)
  • Author(s): Hiroki Kondo
  • Organizer: International Workshop on Symmetry and Topology in Condensed-Matter Physics
  • Int'l Joint Research
• [Presentation] Z2 topological invariant for magnon spin Hall systems (2018)
  • Author(s): Hiroki Kondo
  • Organizer: BEC2018X
  • Int'l Joint Research
• [Presentation] Majorana excitations in Kitaev spin liquids (2018)
  • Author(s): Hosho Katsura
  • Organizer: SAMAHANG PISIKA NG PILIPINAS Physics Society of the Philippines
  • Int'l Joint Research / Invited
• [Presentation] Z2 topological invariants of fermionic and bosonic insulators (2018)
  • Author(s): Hosho Katsura
  • Organizer: Progress in the Mathematics of Topological States of Matter
  • Int'l Joint Research / Invited
• [Presentation] Z2 invariant for topological magnon insulators (2018)
  • Author(s): Hosho Katsura
  • Organizer: Quantum Magnetism: Frustration, Low-dimensionality, Topology
  • Int'l Joint Research / Invited
• [Presentation] マグノンスピンホール系におけるZ2トポロジカル不変量 (2018)
  • Author(s): 近藤寛記
  • Organizer: 日本物理学会 2018年秋季大会
• [Presentation] マグノンスピンホール系における Z2トポロジカル不変量 (2018)
  • Author(s): 近藤寛記
  • Organizer: 基研研究会「スピン系物理の最前線」
• [Remarks] Katsura group Homepage
  • URL: http://park.itc.u-tokyo.ac.jp/hkatsura-lab/