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Studies of topological phases based on lattice gauge theories

Research Project

Project/Area Number 25400388
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionIbaraki University

Principal Investigator

Fukui Takahiro  茨城大学, 理学部, 教授 (10322009)

Project Period (FY) 2013-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsトポロジカル絶縁体 / 第1チャーン数 / エンタングルメント / ストレーダ公式 / 第2チャーン数 / 量子ホール効果 / トポロジカルポンプ / Streda公式 / スピンポンプ / 量子異常 / トポロジカル超伝導体 / チャーン数 / エンタングルメント・チャーン数 / エンタングルメント・トポロジカル数 / 超格子 / ベリー位相
Outline of Final Research Achievements

The topological insulator is a new type of insulator. Let us consider a simple model which has the trivial Chern number because of time-reversal symmetry. Even if the total Chern number is zero, there is the case where each spin sector, if such a division is possible, has a nontrivial Chern number. Thus, vanishing Chern number does not necessarily mean that the system is topologically trivial.
Motivated by such an observation, we have started our research by proposing and analyzing a super lattice model which is a layered system with opposite Chern numbers. To understand unique properties of the model in spite of the vanishing Chern number, we have invented a new topological number "entanglement Chern number". It has turned out that such a new number is successfully applied to the description of generic topological phases of the systems.

Report

(5 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (20 results)

All 2017 2016 2015 2014 2013

All Journal Article (8 results) (of which Peer Reviewed: 8 results,  Acknowledgement Compliant: 7 results,  Open Access: 5 results) Presentation (12 results)

  • [Journal Article] Bulk-edge correspondence in topological pumping2016

    • Author(s)
      Y. Hatsugai, and T. Fukui
    • Journal Title

      Phys. Rev. B

      Volume: 94 Issue: 4 Pages: 41102-41102

    • DOI

      10.1103/physrevb.94.041102

    • NAID

      120007135324

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A Spin Pump Characterized by Entanglement Chern Numbers2016

    • Author(s)
      T. Fukui and Y. Hatsugai
    • Journal Title

      J. Phys. Soc. Jpn.

      Volume: 85 Issue: 8 Pages: 83703-83703

    • DOI

      10.7566/jpsj.85.083703

    • NAID

      130006245658

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Streda formula for the Hofstadter-Wilson-Dirac model in two and four dimensions2016

    • Author(s)
      T. Fukui and T. Fujiwara
    • Journal Title

      J. Phys. Soc. Jpn.

      Volume: 85 Issue: 12 Pages: 124709-124709

    • DOI

      10.7566/jpsj.85.124709

    • NAID

      130006710554

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Entanglement Chern Number of the Kane–Mele Model with Ferromagnetism2016

    • Author(s)
      H. Araki, T. Kariyado, T. Fukui and Y. Hatsugai
    • Journal Title

      J. Phys. Soc. Jpn.

      Volume: 85 Issue: 4 Pages: 43706-43706

    • DOI

      10.7566/jpsj.85.043706

    • NAID

      120007134638

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Disentangled topological numbers by a purification of entangled mixed states for non-interacting2015

    • Author(s)
      T. Fukui and Y. Hatsugai
    • Journal Title

      J. Phys. Soc. Jpn.

      Volume: 84 Issue: 4 Pages: 0437031-6

    • DOI

      10.7566/jpsj.84.043703

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Characterizing the weak topological properties: Berry phase point of view2014

    • Author(s)
      Y. Yoshimura, K.-I. Imura, T. Fukui, and Y. Hatsugai
    • Journal Title

      Phys. Rev. B

      Volume: 90 Issue: 15

    • DOI

      10.1103/physrevb.90.155443

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Entanglement Chern number for an extensive partition of a topological ground state2014

    • Author(s)
      T. Fukui and Y. Hatsugai
    • Journal Title

      J. Phys. Soc. Jpn.

      Volume: 83 Issue: 11 Pages: 1137051-7

    • DOI

      10.7566/jpsj.83.113705

    • NAID

      40020264793

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] T. Fukui, K.-I. Imura and Y. Hatsugai2013

    • Author(s)
      T. Fukui, K.-I. Imura and Y. Hatsugai
    • Journal Title

      Journal of the Physical Society of Japan

      Volume: 82 Issue: 7 Pages: 073708-073708

    • DOI

      10.7566/jpsj.82.073708

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] 2次元・4次元のHofstadter-Wilson-Dirac模型とStreda公式2017

    • Author(s)
      福井隆裕, 藤原高徳
    • Organizer
      日本物理学会 第72回年次大会
    • Place of Presentation
      大阪大学 豊中キャンパス
    • Year and Date
      2017-03-17
    • Related Report
      2016 Annual Research Report
  • [Presentation] トポロジカル量子ポンプにおけるバルクエッジ対応2017

    • Author(s)
      吉村幸徳, 井村健一郎, 初貝安弘, 福井隆裕
    • Organizer
      日本物理学会 第72回年次大会
    • Place of Presentation
      大阪大学 豊中キャンパス
    • Year and Date
      2017-03-17
    • Related Report
      2016 Annual Research Report
  • [Presentation] エンタングルメント・チャーン数で特徴付けられるスピン・ポンプ2016

    • Author(s)
      福井隆裕, 初貝安弘
    • Organizer
      日本物理学会 2016年秋季大会
    • Place of Presentation
      金沢大学 角間キャンパス
    • Year and Date
      2016-09-13
    • Related Report
      2016 Annual Research Report
  • [Presentation] トポロジカルポンプにおけるバルク・エッジ対応2016

    • Author(s)
      初貝安弘, 福井隆裕
    • Organizer
      日本物理学会第71回年次大会
    • Place of Presentation
      東北学院大学
    • Year and Date
      2016-03-19
    • Related Report
      2015 Research-status Report
  • [Presentation] 1次元梯子系におけるスピン・ポンプとエンタングルメント・チャーン数2015

    • Author(s)
      福井隆裕,初貝安弘
    • Organizer
      日本物理学会2015年秋季大会
    • Place of Presentation
      関西大
    • Year and Date
      2015-09-16
    • Related Report
      2015 Research-status Report
  • [Presentation] 磁場下のKane-Mele模型のエンタングルメントチャーン数と新しい相2015

    • Author(s)
      荒木広夢, 苅宿俊風, 福井隆裕, 初貝安弘
    • Organizer
      日本物理学会2015年秋季大会
    • Place of Presentation
      関西大
    • Year and Date
      2015-09-16
    • Related Report
      2015 Research-status Report
  • [Presentation] エンタングルメント・チャーン数の提案と応用2015

    • Author(s)
      福井隆裕,初貝安弘
    • Organizer
      日本物理学会 第70回年次大会
    • Place of Presentation
      早稲田大学早稲田キャンパス
    • Year and Date
      2015-03-21 – 2015-03-24
    • Related Report
      2014 Research-status Report
  • [Presentation] 必ずしもカイラルでない系におけるベリー位相の量子化2014

    • Author(s)
      福井隆裕,初貝安弘
    • Organizer
      日本物理学会 2014年秋季大会
    • Place of Presentation
      中部大学春日井キャンパス
    • Year and Date
      2014-09-07 – 2014-09-10
    • Related Report
      2014 Research-status Report
  • [Presentation] 超格子系の弱トポロジカル相とエッジ状態2014

    • Author(s)
      吉村幸徳,井村健一郎,福井隆裕,初貝安弘
    • Organizer
      日本物理学会 第69回年次大会
    • Place of Presentation
      東海大学湘南キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] 一次元トポロジカル絶縁体とトポロジカル超格子絶縁体2013

    • Author(s)
      岡本真由子,井村健一郎,高根美武,福井隆裕,初貝安弘
    • Organizer
      日本物理学会 2013年秋季大会
    • Place of Presentation
      徳島大学常三島キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] 時間反転対称性を破る格子ディラック模型の離散対称性と量子化2013

    • Author(s)
      初貝安弘,福井隆裕,井村健一郎
    • Organizer
      日本物理学会 2013年秋季大会
    • Place of Presentation
      徳島大学常三島キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] 二次元超格子系におけるトポロジカル相2013

    • Author(s)
      福井隆裕,井村健一郎,初貝安弘
    • Organizer
      日本物理学会 2013年秋季大会
    • Place of Presentation
      徳島大学常三島キャンパス
    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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