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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

Publicly Offered Research

Project AreaDiscrete 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 TypeSingle-year Grants
Research InstitutionThe 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 *help
¥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。

Report

(2 results)
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • Research Products

    (48 results)

All 2020 2019 2018 Other

All Int'l Joint Research (2 results) Journal Article (15 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 14 results,  Open Access: 1 results) Presentation (30 results) (of which Int'l Joint Research: 22 results,  Invited: 8 results) Remarks (1 results)

  • [Int'l Joint Research] ダブリン高等研究所(アイルランド)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Utrecht University(オランダ)

    • Related Report
      2018 Annual Research Report
  • [Journal Article] Simulating quantum circuits by adiabatic computation: Improved spectral gap bounds2020

    • 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

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Onsager’s Scars in Disordered Spin Chains2020

    • 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

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dissipative spin chain as a non-Hermitian Kitaev ladder2019

    • Author(s)
      Shibata Naoyuki、Katsura Hosho
    • Journal Title

      Physical Review B

      Volume: 99 Issue: 17

    • DOI

      10.1103/physrevb.99.174303

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dissipative quantum Ising chain as a non-Hermitian Ashkin-Teller model2019

    • Author(s)
      Shibata Naoyuki、Katsura Hosho
    • Journal Title

      Physical Review B

      Volume: 99 Issue: 22

    • DOI

      10.1103/physrevb.99.224432

    • NAID

      130008152905

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Three-dimensional topological magnon systems2019

    • Author(s)
      Kondo Hiroki、Akagi Yutaka、Katsura Hosho
    • Journal Title

      Physical Review B

      Volume: 100 Issue: 14

    • DOI

      10.1103/physrevb.100.144401

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ferromagnetism in the SU(n) Hubbard model with a nearly flat band2019

    • Author(s)
      Tamura Kensuke、Katsura Hosho
    • Journal Title

      Physical Review B

      Volume: 100 Issue: 21

    • DOI

      10.1103/physrevb.100.214423

    • Related Report
      2019 Annual Research Report
    • 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

    • Related Report
      2019 Annual Research Report
  • [Journal Article] Z(2) topological invariant for magnon spin Hall systems2019

    • 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

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rigorous Results for the Ground States of the Spin-2 Bose-Hubbard Model2019

    • Author(s)
      Yang Hong、Katsura Hosho
    • Journal Title

      Physical Review Letters

      Volume: 122 Issue: 5

    • DOI

      10.1103/physrevlett.122.053401

    • NAID

      130007736183

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Supersymmetry breaking and Nambu-Goldstone fermions in interacting Majorana chains2019

    • Author(s)
      Sannomiya Noriaki、Katsura Hosho
    • Journal Title

      Physical Review D

      Volume: 99 Issue: 4 Pages: 045002-045002

    • DOI

      10.1103/physrevd.99.045002

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Transforming generalized Ising models into Boltzmann machines2019

    • 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

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Learning disordered topological phases by statistical recovery of symmetry2018

    • 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

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Parity-time-symmetric topological superconductor2018

    • 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

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Exact ground states for interacting Kitaev chains2018

    • Author(s)
      Wouters Jurriaan、Katsura Hosho、Schuricht Dirk
    • Journal Title

      Physical Review B

      Volume: 98 Issue: 15

    • DOI

      10.1103/physrevb.98.155119

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models2018

    • 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

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Presentation] Three-dimensional topological magnon systems2020

    • Author(s)
      Hiroki Kondo
    • Organizer
      APS March Meeting 2020, online
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Haldane Phase in Spin-1 Bose-Hubbard Model with Flat Band2020

    • Author(s)
      Hong Yang
    • Organizer
      APS March Meeting 2020, online
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Dissipative quantum Ising chain as a non-Hermitian Ashkin-Teller model2020

    • Author(s)
      Naoyuki Shibata
    • Organizer
      APS March Meeting 2020, online
    • Related Report
      2019 Annual Research Report
    • 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
    • Related Report
      2019 Annual Research Report
  • [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)
    • Related Report
      2019 Annual Research Report
  • [Presentation] Topological invariants and surface states in magnon systems2019

    • Author(s)
      Hiroki Kondo
    • Organizer
      Topological phase workshop, Sendai
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Integrable dissipative spin chains2019

    • Author(s)
      Naoyuki Shibata
    • Organizer
      IIS-Chiba Workshop NH2019, Kashiwa
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Rigorous Results on the Ground States of the Spin-2 Bose-Hubbard Model2019

    • Author(s)
      Hong Yang and Hosho Katsura
    • Organizer
      The Fourth Kyoto-Beijing-Tokyo Workshop on Ultracold Atomic Gases, YITP, Kyoto
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Integrable dissipative spin chains2019

    • Author(s)
      Naoyuki Shibata and Hosho Katsura
    • Organizer
      Thermalization, Many body localization and Hydrodynamics, ICTS, Bangalore
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Rigorous Results on the Ground States of the Spin-2 Bose-Hubbard Model2019

    • Author(s)
      Hong Yang and Hosho Katsura
    • Organizer
      Thermalization, Many body localization and Hydrodynamics, ICTS, Bangalore
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Three-dimensional topological magnon systems2019

    • Author(s)
      Hiroki Kondo
    • Organizer
      International Conference on Topological Materials Science 2019 (TopoMat2019), Kyoto
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Frustration-free Majorana fermion models2019

    • Author(s)
      Hosho Katsura
    • Organizer
      Interacting Majorana Fermions, University of Britich Columbia, Vancouver
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Supersymmetry breaking and Nambu-Goldstone fermions in lattice models2019

    • Author(s)
      Hosho Katsura
    • Organizer
      KIAS Workshop on Topology and Correlation in Quantum Materials, Busan
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Integrable dissipative spin chains2019

    • Author(s)
      Hosho Katsura
    • Organizer
      Amsterdam Summer Workshop on Low-D Quantum Condensed Matter 2019, Amsterdam
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Integrable dissipative spin chains2019

    • Author(s)
      Hosho Katsura
    • Organizer
      Topological phase workshop, Sendai
    • Related Report
      2019 Annual Research Report
    • 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
    • Related Report
      2019 Annual Research Report
  • [Presentation] The Haldane Phase of Spinful Bosons with Flat Band2019

    • 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
    • Related Report
      2019 Annual Research Report
  • [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
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Z2 topological invariant for magnon spin Hall systems2019

    • Author(s)
      Hiroki Kondo
    • Organizer
      Topological Phases and Functionality of Correlated Electron Systems 2019 (TPFC2019)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Z2 topological invariant for magnon spin Hall systems2019

    • Author(s)
      Hiroki Kondo
    • Organizer
      APS March Meeting 2019
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Z2 invariants for disordered topological insulators and superconductors2019

    • Author(s)
      Hosho Katsura
    • Organizer
      Theoretical studies of topological phases of matter
    • Related Report
      2018 Annual Research Report
    • 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
    • Related Report
      2018 Annual Research Report
  • [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
    • Related Report
      2018 Annual Research Report
  • [Presentation] Z2 Topological Invariant for Magnon Spin Hall Systems2018

    • Author(s)
      Hiroki Kondo
    • Organizer
      International Workshop on Symmetry and Topology in Condensed-Matter Physics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Z2 topological invariant for magnon spin Hall systems2018

    • Author(s)
      Hiroki Kondo
    • Organizer
      BEC2018X
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Majorana excitations in Kitaev spin liquids2018

    • Author(s)
      Hosho Katsura
    • Organizer
      SAMAHANG PISIKA NG PILIPINAS Physics Society of the Philippines
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Z2 topological invariants of fermionic and bosonic insulators2018

    • Author(s)
      Hosho Katsura
    • Organizer
      Progress in the Mathematics of Topological States of Matter
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Z2 invariant for topological magnon insulators2018

    • Author(s)
      Hosho Katsura
    • Organizer
      Quantum Magnetism: Frustration, Low-dimensionality, Topology
    • Related Report
      2018 Annual Research Report
    • 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
    • Related Report
      2018 Annual Research Report
  • [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」
    • Related Report
      2018 Annual Research Report
  • [Remarks] Katsura group Homepage

    • URL

      http://park.itc.u-tokyo.ac.jp/hkatsura-lab/

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report

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Published: 2018-04-23   Modified: 2021-01-27  

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