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Research about supersymmetric higher dimensional non-commutative geometry and topologial quantum many-body states

Research Project

Project/Area Number 23740212
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Particle/Nuclear/Cosmic ray/Astro physics
Research InstitutionKagawa National College of Technology

Principal Investigator

HASEBE Kazuki  香川高等専門学校, 一般教育科, 講師 (60435469)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords非可換幾何 / 量子スピン系 / トポロジカル絶縁体 / 非エルミート量子力学 / 超対称性 / 南部括弧 / 南部代数 / 国際研究者交流(アメリカ) / 国際情報交流(アメリカ)
Research Abstract

We established supersymmetric higher dimensional non-commutative geomery and applied its mathematics to the topological matters. In 2011, we explored non-commutative geometry for supersymmetric higher dimensional spheres and hyperboloids. Besides, we applied the mathematics to the supersymmetric quantum spin systems and non-Hermitian quantum mechanics and exploited their topological structures such as edge states and hidden order. In 2012, we further investigated the supersymmetric quantum spin systems especially about the recently proposed quantum entanglement. In 2013, we applied the non-commutative geometry to the topological insulators (in particular A-class nad AIII-class) and analyzed their physical properties.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (36 results)

All 2013 2012 2011 Other

All Journal Article (15 results) (of which Peer Reviewed: 14 results) Presentation (21 results) (of which Invited: 5 results)

  • [Journal Article] Topological many-body states in quantum antiferromagnets via fuzzy super-geometry2013

    • Author(s)
      Kazuki Hasebe, Keisuke Totsuka
    • Journal Title

      Symmetry

      Volume: 5 Pages: 119-214

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Quantum entanglement and topological order in hole-doped valence bond solid states2013

    • Author(s)
      Kazuki Hasebe, Keisuke Totsuka
    • Journal Title

      Phys. Rev. B

      Volume: 87 Pages: 45115-45115

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Quantum Entanglement and Topological Order in Hole-Doped Valence Bond Solid States2013

    • Author(s)
      Kazuki Hasebe, Keisuke Totsuka
    • Journal Title

      Physical Review B

      Volume: 87 Issue: 4

    • DOI

      10.1103/physrevb.87.045115

    • Related Report
      2013 Annual Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry2013

    • Author(s)
      Kazuki Hasebe, Keisuke Totsuka
    • Journal Title

      Symmetry

      Volume: in press

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Non-compact Hopf maps and fuzzy ultra-hyperboloids2012

    • Author(s)
      Kazuki Hasebe
    • Journal Title

      Nucl.Phys. B

      Volume: 865 Pages: 148-199

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Fuzzy super-geometry and topological many-body states2012

    • Author(s)
      Kazuki Hasebe
    • Journal Title

      素粒子論研究

      Volume: vol.12

    • Related Report
      2013 Final Research Report
  • [Journal Article] Time-reversal symmetry in non-Hermitian systems2012

    • Author(s)
      Masatoshi Sato, Kazuki Hasebe, Kenta Esaki, Mahito Kohmoto
    • Journal Title

      Prog.T heor. Phys

      Volume: 127 Pages: 937-974

    • NAID

      40019319854

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Time-Reversal Symmetry in Non-Hermitian Systems2012

    • Author(s)
      Masatoshi Sato, Kazuki Hasebe, Kenta Esaki, Mahito Kohmoto
    • Journal Title

      Progress of Theoretical Physics

      Volume: 127 Pages: 937-974

    • NAID

      40019319854

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Non-Compact Hopf Maps and Fuzzy Ultra-Hyperboloids2012

    • Author(s)
      Kazuki Hasebe
    • Journal Title

      Nuclear Physics B

      Volume: 865 Issue: 1 Pages: 148-199

    • DOI

      10.1016/j.nuclphysb.2012.07.017

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Edge states and topological phases in non-Hermitian systems2011

    • Author(s)
      Kenta Esaki, Masatoshi Sato, Kazuki Hasebe, Mahito Kohmoto
    • Journal Title

      Phys. Rev. B

      Volume: 84 Pages: 205128-205128

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Graded Hopf maps and fuzzy superspheres2011

    • Author(s)
      Kazuki Hasebe
    • Journal Title

      Nucl. Phys. B

      Volume: 853 Pages: 777-827

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hidden order and dyamics in supersymmetric valence bond solid state formalism2011

    • Author(s)
      Kazuki Hasebe, Keisuke Totsuka
    • Journal Title

      Phys. Rev. B

      Volume: 84 Pages: 104426-104426

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Graded Hopf maps and fuzzy superspheres2011

    • Author(s)
      長谷部一気
    • Journal Title

      Nuclear Physics B

      Volume: vol.853 Pages: 777-827

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Hidden order and dynamics in supersymmetric valence-bond solid states2011

    • Author(s)
      長谷部一気、戸塚圭介
    • Journal Title

      Physical Review B

      Volume: vol.84 Issue: 10

    • DOI

      10.1103/physrevb.84.104426

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Edge states and topological phases in non-Hermitian systems2011

    • Author(s)
      K.Esaki, M.Sato, K.Hasebe, M.Kohmoto
    • Journal Title

      Physical Review B

      Volume: 84 Issue: 20

    • DOI

      10.1103/physrevb.84.205128

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Non-commutative geometry and quantum Hall effect in any dimensions2013

    • Author(s)
      長谷部 一気
    • Organizer
      Exotic space-time geometry and its applications
    • Place of Presentation
      理化学研究所(埼玉 和光)
    • Year and Date
      2013-02-23
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Non-commutative geometry in higher dimensional quantum Hall effect as A-class topological insulator2013

    • Author(s)
      Kazuki Hasebe
    • Organizer
      Workshop on Noncommutative field theory and gravity
    • Place of Presentation
      Corfu, Greece
    • Related Report
      2013 Final Research Report
  • [Presentation] Non-commutative geometry in higher dimensional quantum Hall effect as A-class topological insulator2013

    • Author(s)
      長谷部 一気
    • Organizer
      「Noncommutative field theory and gravity」
    • Place of Presentation
      ギリシャ コルフ島
    • Related Report
      2013 Annual Research Report
  • [Presentation] Noncommutative Geometry and Quantum Hall Effect in Any Dimensions2013

    • Author(s)
      Kazuki Hasebe
    • Organizer
      エキゾチック時空幾何とその応用
    • Place of Presentation
      理化学研究所(和光)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 非コンパクトなホップ写像とファジーな双曲多様体2012

    • Author(s)
      長谷部 一気
    • Organizer
      日本物理学会2012年秋季大会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2012-09-11
    • Related Report
      2013 Final Research Report
  • [Presentation] Quantum Antiferromagnets from fuzzy (super-)geometry2012

    • Author(s)
      長谷部 一気
    • Organizer
      四国セミナー
    • Place of Presentation
      高知大学
    • Related Report
      2013 Final Research Report
  • [Presentation] Quantum Antiferromagnets from fuzzy super-geometry2012

    • Author(s)
      Kazuki Hasebe
    • Organizer
      Supersymmetry in Integrable systems-SIS
    • Place of Presentation
      Yerevan Armenia
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Quantum Antiferromagnets from Fuzzy Super-Geometry2012

    • Author(s)
      Kazuki Hasebe
    • Organizer
      Supersymmetry and Integrable Systems '12
    • Place of Presentation
      アルメニア エレバン大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Non-Compact Hopf Maps and Fuzzy Ultra-Hyperboloids2012

    • Author(s)
      Kazuki Hasebe
    • Organizer
      日本物理学会 秋季大会
    • Place of Presentation
      京都産業大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Quantum Antiferromagnets from Fuzzy Super-Geometry2012

    • Author(s)
      Kazuki Hasebe
    • Organizer
      四国セミナー
    • Place of Presentation
      高知大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Supersymmetry and higher dimensional fuzzy supersphere2011

    • Author(s)
      長谷部 一気
    • Organizer
      四国セミナー
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Final Research Report
  • [Presentation] Supersymmetric valence bond solid states and generalized hidden order2011

    • Author(s)
      Kazuki Hasebe
    • Organizer
      Novel quantum states in condensed matter
    • Place of Presentation
      京都大学 基礎物理学研究所
    • Related Report
      2013 Final Research Report
  • [Presentation] 超対称なバレンスボンド状態におけるエンタングルメントと端状態2011

    • Author(s)
      長谷部 一気
    • Organizer
      日本物理学会2011年秋季大会
    • Place of Presentation
      富山大学
    • Related Report
      2013 Final Research Report
  • [Presentation] 一般化されたホップ写像とファジー多様体2011

    • Author(s)
      長谷部 一気
    • Organizer
      日本物理学会2011年秋季大会
    • Place of Presentation
      弘前大学
    • Related Report
      2013 Final Research Report
  • [Presentation] Generalized Hopf maps and fuzzy manifolds2011

    • Author(s)
      Kazuki Hasebe
    • Organizer
      Supersymmetry in Integrable systems-SIS'11
    • Place of Presentation
      Hannover, Germany
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Fuzzy super-geometry and topological many-body states2011

    • Author(s)
      長谷部 一気
    • Organizer
      場の理論と弦理論
    • Place of Presentation
      京都大学 基礎物理学研究所
    • Related Report
      2013 Final Research Report
  • [Presentation] Fuzzy super-geometry and topological many-body states

    • Author(s)
      長谷部一気
    • Organizer
      場の理論と弦理論研究会
    • Place of Presentation
      京都大学基礎物理学研究所
    • Related Report
      2011 Research-status Report
  • [Presentation] Generalized Hopf maps and fuzzy manifolds

    • Author(s)
      長谷部一気
    • Organizer
      supersymmetry and integrable systems(招待講演)
    • Place of Presentation
      ドイツ ハノーバー
    • Related Report
      2011 Research-status Report
  • [Presentation] 一般化されたホップ写像と非可換多様体

    • Author(s)
      長谷部一気
    • Organizer
      日本物理学会秋季大会
    • Place of Presentation
      弘前大学
    • Related Report
      2011 Research-status Report
  • [Presentation] 超対称バレンスボンド状態においてエンタングルメントと端状態

    • Author(s)
      長谷部一気
    • Organizer
      日本物理学会秋季大会
    • Place of Presentation
      富山大学
    • Related Report
      2011 Research-status Report
  • [Presentation] supersymmetric valence bond solid states and generalized hidden order

    • Author(s)
      長谷部一気
    • Organizer
      西宮湯川国際研究会``novel quantum states in condensed matter''
    • Place of Presentation
      京都大学基礎物理学研究所
    • Related Report
      2011 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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