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Entanglement Structure Analysis of Non-Uniform Systems by Tensor Network Formulation

Research Project

Project/Area Number 17K05578
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 InstitutionKobe University

Principal Investigator

Nishino Tomotoshi  神戸大学, 理学研究科, 准教授 (00241563)

Project Period (FY) 2017-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsエンタングルメント / テンソルネットワーク / 繰り込み群 / エントロピー / フラクタル / ランダム系 / 相転移 / 臨界指数 / 非一様系 / 多面体模型 / 中心電荷 / 非一様 / 相互情報量 / 量子エントロピー / 臨界現象 / HOTRG / イジングモデル / 木構造 / 特異値分解 / ディスエンタングラー / 階層
Outline of Final Research Achievements

Structure contained in the quantum entanglement is studied through the tensor network formulation. To classical and statistical spin models defined on the latices with fractal geometry, we applied the higher-order tensor renormalization group (HOTRG) method, and showed that the systems exhibit second-order phase transitions. The obtained value of the critical indices are non-trivial. To the random bond Ising model on square lattice, we applied the time evolving block decimation (TEBD) method. It was clarified that the entanglement entropy defined for the boundary spin configuration function exhibit critical singularity, even on the Nishimori curve. To the polyhedral vector spin models on the square lattice, we applied the corner transfer matrix renormalization group (CTMRG) method, and clarified that the systems exhibit second-order phase transition, where the value of the central charge is larger than unity for the dodecahedron and icosahedron models.

Academic Significance and Societal Importance of the Research Achievements

フラクタル格子上では臨界領域でもエンタングルメントの増大が抑制され、テンソルネットワーク形式による相転移解析が数値的に精密に行えることが判明し、フラクタル系の実質的な空間次元の理解が深まると期待される。2次元格子上のランダムスピン系に対してTEBD手法による精密解析が可能であることが実証されたことから、より高次元のランダム系へのテンソルネットワーク形式の応用が広がり、スピングラスまでを含む状態解析が期待される。以上の成果などをレビュー図書に取りまとめ、初学者向けの解説も含めたものを出版した。より多彩な物理系へのテンソルネットワークの応用が更に広がって行くことが期待される。

Report

(5 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (18 results)

All 2021 2020 2019 2018 2017 Other

All Int'l Joint Research (2 results) Journal Article (6 results) (of which Int'l Joint Research: 5 results,  Peer Reviewed: 6 results,  Open Access: 1 results) Presentation (8 results) Remarks (1 results) Funded Workshop (1 results)

  • [Int'l Joint Research] スロバキア科学アカデミー(スロバキア)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] スロバキア科学アカデミー(スロバキア)

    • Related Report
      2018 Research-status Report
  • [Journal Article] Entanglement Entropy on the Boundary of the Square-Lattice ±J Ising Model2020

    • Author(s)
      Sasagawa Yoshinori、Ueda Hiroshi、Genzor Jozef、Gendiar Andrej、Nishino Tomotoshi
    • Journal Title

      Journal of the Physical Society of Japan

      Volume: 89 Issue: 11 Pages: 114005-114005

    • DOI

      10.7566/jpsj.89.114005

    • NAID

      120006919995

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Corner transfer matrix renormalization group analysis of the two-dimensional dodecahedron model2020

    • Author(s)
      Ueda Hiroshi、Okunishi Kouichi、Yunoki Seiji、Nishino Tomotoshi
    • Journal Title

      Physical Review E

      Volume: 102 Issue: 3 Pages: 032130-032130

    • DOI

      10.1103/physreve.102.032130

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Entanglement-entropy study of phase transitions in six-state clock model2020

    • Author(s)
      Roman Crcmar, Andrej Gendiar, Tomotoshi Nishino
    • Journal Title

      Acta Physica Polonica A

      Volume: 137 Pages: 1-4

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Finite-m scaling analysis of Berezinskii-Kosterlitz-Thouless phase transitions and entanglement spectrum for the six-state clock model2020

    • Author(s)
      Ueda Hiroshi、Okunishi Kouichi、Harada Kenji、Krcmar Roman、Gendiar Andrej、Yunoki Seiji、Nishino Tomotoshi
    • Journal Title

      Physical Review E

      Volume: 101 Issue: 6 Pages: 062111-062111

    • DOI

      10.1103/physreve.101.062111

    • NAID

      120006865707

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Tensor-network study of a quantum phase transition on the Sierpi?ski fractal2018

    • Author(s)
      Krcmar Roman、Genzor Jozef、Lee Yoju、?en?arikov? Hana、Nishino Tomotoshi、Gendiar Andrej
    • Journal Title

      Physical Review E

      Volume: 98 Issue: 6 Pages: 1-8

    • DOI

      10.1103/physreve.98.062114

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Critical behavior of the two-dimensional icosahedron model2017

    • Author(s)
      Ueda Hiroshi、Okunishi Kouichi、Krcmar Roman、Gendiar Andrej、Yunoki Seiji、Nishino Tomotoshi
    • Journal Title

      Physical Review E

      Volume: 96 Issue: 6 Pages: 1-5

    • DOI

      10.1103/physreve.96.062112

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] ☆フェルミ系☆のエネルギー変形あれこれと境界効果の↓抑制↓2021

    • Author(s)
      西野友年
    • Organizer
      日本物理学会第76回年次大会
    • Related Report
      2020 Annual Research Report
  • [Presentation] 1次か2次かの examination 目標は octahedron model2020

    • Author(s)
      西野友年
    • Organizer
      日本物理学会2020年秋季大会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Tree Tensor Network を用いた量子系の最適表現 I2020

    • Author(s)
      橋本豊、西野友年
    • Organizer
      日本物理学会第75回年次大会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Tree Tensor Network を用いた量子系の最適表現 II2020

    • Author(s)
      西野友年、橋本豊
    • Organizer
      日本物理学会第75回年次大会
    • Related Report
      2020 Annual Research Report
  • [Presentation] フラクタル格子上のイジング模型2019

    • Author(s)
      西野友年
    • Organizer
      日本物理学会分科会
    • Related Report
      2019 Research-status Report
  • [Presentation] Tree Tensor Network を用いた量子系の最適表現 I2019

    • Author(s)
      西野友年
    • Organizer
      日本物理学会年会
    • Related Report
      2019 Research-status Report
  • [Presentation] 謝爾賓斯基 (Sierpinski) 三角形上の横磁場イジングを HOTRG で調べてみた2019

    • Author(s)
      西野友年
    • Organizer
      日本物理学会第74回年次大会
    • Related Report
      2018 Research-status Report
  • [Presentation] シェルピンスキーのホットカーペットにイジング乗せてみた2018

    • Author(s)
      西野友年
    • Organizer
      日本物理学会2018年秋季大会
    • Related Report
      2018 Research-status Report
  • [Remarks] DMRG Home Page

    • URL

      http://quattro.phys.sci.kobe-u.ac.jp/dmrg.html

    • Related Report
      2020 Annual Research Report 2019 Research-status Report 2018 Research-status Report
  • [Funded Workshop] Tensor Network State: Algorithms and Applications 20182018

    • Related Report
      2018 Research-status Report

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Published: 2017-04-28   Modified: 2022-01-27  

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