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Study of finite temperature properties of frustrated spin systems by tensor network approach

Research Project

Project/Area Number 19K03740
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 13030:Magnetism, superconductivity and strongly correlated systems-related
Research InstitutionThe University of Tokyo

Principal Investigator

Okubo Tsuyoshi  東京大学, 大学院理学系研究科(理学部), 特任准教授 (00514051)

Project Period (FY) 2019-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2019: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywordsテンソルネットワーク / 量子スピン液体 / キタエフ模型 / 相転移 / フラストレーション / スピン液体 / フラストレート磁性体 / 熱ホール伝導度 / 密度行列 / 有限温度物性 / 量子スピン / 磁性体
Outline of Research at the Start

本研究では、相互作用にフラストレーションが存在する磁性体、フラストレート磁性体に着目し、その物性、特に有限温度での種々の物理量をテンソルネットワーク法により数値的に解析する。精度の高い有限温度での計算手法を開発することで、実験研究とモデル計算の直接比較を可能にし、フラストレート量子スピン系を対象に、量子スピン液体などの新規秩序を基底状態と有限温度の双方の視点から物性を理解することを目的とする。これまで波動関数のテンソルネットワーク表現により非常に大きな系の基底状態計算を可能にしてきた手法を、密度行列による有限温度に拡張し、フラストレート磁性体の物理を理解するために新しい軸を展開する。

Outline of Final Research Achievements

In this study, we have developed a method to analyze finite temperature properties of two-dimensional frustrated magnets using tensor network representations, and applied it to Kitaev spin liquid. The density matrix of a finite-temperature quantum state is described by a tensor network. We employed an infinite two-dimensional tensor product operator, iTPO, for an infinite sytem, and a matrix product operator, MPO, for a finite two-dimensional system. In particular, we showed the temperature dependence of the thermal Hall conductivity in Kitaev spin liquid under a magnetic field, and the effect of off-diagonal interactions to finite temperature properties.

Academic Significance and Societal Importance of the Research Achievements

本研究により、これまでは高精度な解析が困難であった、二次元フラストレート磁性体の有限温度物性を、テンソルネットワークを用いて解析する手法が確立された。従来から実用化されているテンソルネットワークによる基底状態の計算と、本研究による有限温度物性の計算を組み合わせることで、スピン液体等のフラストレート磁性体で実現する新奇秩序の物性を、基底状態で顕著な量子揺らぎ、有限温度で現れる温度揺らぎの、双方の視点から解析できるようになる。開発した手法により、特に、磁場中のキタエフスピン液体における熱ホール伝導度の温度依存性について、理解が進み、この成果は、今後のキタエフ物質の物性理解にもつながると考えている。

Report

(5 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • Research Products

    (53 results)

All 2023 2022 2021 2020 2019 Other

All Int'l Joint Research (2 results) Journal Article (11 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 11 results,  Open Access: 4 results) Presentation (40 results) (of which Int'l Joint Research: 13 results,  Invited: 13 results)

  • [Int'l Joint Research] University of Toronto/Perimeter Institute(カナダ)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Korea University(韓国)

    • Related Report
      2019 Research-status Report
  • [Journal Article] TeNeS: Tensor network solver for quantum lattice systems2022

    • Author(s)
      Motoyama Yuichi、Okubo Tsuyoshi、Yoshimi Kazuyoshi、Morita Satoshi、Kato Takeo、Kawashima Naoki
    • Journal Title

      Computer Physics Communications

      Volume: 279 Pages: 1084371-08437

    • DOI

      10.1016/j.cpc.2022.108437

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Bond-weighted tensor renormalization group2022

    • Author(s)
      Adachi Daiki、Okubo Tsuyoshi、Todo Synge
    • Journal Title

      Physical Review B

      Volume: 105 Issue: 6

    • DOI

      10.1103/physrevb.105.l060402

    • NAID

      130008156600

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Quantum critical phenomena in a spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> frustrated square lattice with spatial anisotropy2021

    • Author(s)
      Yamaguchi H.、Iwasaki Y.、Kono Y.、Okubo T.、Miyamoto S.、Hosokoshi Y.、Matsuo A.、Sakakibara T.、Kida T.、Hagiwara M.
    • Journal Title

      Physical Review B

      Volume: 103 Issue: 22

    • DOI

      10.1103/physrevb.103.l220407

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Gapped ground state in a spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> frustrated square lattice2021

    • Author(s)
      Yamaguchi H.、Uemoto N.、Okubo T.、Kono Y.、Kittaka S.、Sakakibara T.、Yajima T.、Shimono S.、Iwasaki Y.、Hosokoshi Y.
    • Journal Title

      Physical Review B

      Volume: 104 Issue: 6

    • DOI

      10.1103/physrevb.104.l060411

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Phase shift in skyrmion crystals2021

    • Author(s)
      Hayami Satoru、Okubo Tsuyoshi、Motome Yukitoshi
    • Journal Title

      Nature Communications

      Volume: 12 Issue: 1 Pages: 6927-6927

    • DOI

      10.1038/s41467-021-27083-0

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Zero-energy excitation in the classical kagome antiferromagnet NaBa2Mn3F112020

    • Author(s)
      Hayashida Shohei、Ishikawa Hajime、Okamoto Yoshihiko、Okubo Tsuyoshi、Hiroi Zenji、Nilsen G?ran J.、Mutka Hannu、Masuda Takatsugu
    • Journal Title

      Physical Review B

      Volume: 101 Issue: 21

    • DOI

      10.1103/physrevb.101.214409

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Anisotropic tensor renormalization group2020

    • Author(s)
      Adachi Daiki、Okubo Tsuyoshi、Todo Synge
    • Journal Title

      Physical Review B

      Volume: 102 Issue: 5

    • DOI

      10.1103/physrevb.102.054432

    • NAID

      130008152810

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Magnetic field induced quantum phases in a tensor network study of Kitaev magnets2020

    • Author(s)
      Lee Hyun-Yong、Kaneko Ryui、Chern Li Ern、Okubo Tsuyoshi、Yamaji Youhei、Kawashima Naoki、Kim Yong Baek
    • Journal Title

      Nature Communications

      Volume: 11 Issue: 1

    • DOI

      10.1038/s41467-020-15320-x

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Abelian and non-Abelian chiral spin liquids in a compact tensor network representation2020

    • Author(s)
      Lee Hyun-Yong、Kaneko Ryui、Okubo Tsuyoshi、Kawashima Naoki
    • Journal Title

      Physical Review B

      Volume: 101 Issue: 3

    • DOI

      10.1103/physrevb.101.035140

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks2019

    • Author(s)
      Lee Hyun-Yong、Kaneko Ryui、Okubo Tsuyoshi、Kawashima Naoki
    • Journal Title

      Physical Review Letters

      Volume: 123 Issue: 8

    • DOI

      10.1103/physrevlett.123.087203

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Multiple-q states of the J1-J2 classical honeycomb-lattice Heisenberg antiferromagnet under a magnetic field2019

    • Author(s)
      Shimokawa Tokuro、Okubo Tsuyoshi、Kawamura Hikaru
    • Journal Title

      Physical Review B

      Volume: 100 Issue: 22

    • DOI

      10.1103/physrevb.100.224404

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Presentation] テンソルネットワーク法による量子古典エンタングルアルゴリズムの提案2023

    • Author(s)
      大久保毅
    • Organizer
      物性研究のための量子アルゴリズム最前線
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Tensor network representation of Kitaev spin liquid and its application to quantum circuit-based variational calculations2022

    • Author(s)
      Tsuyoshi Okubo
    • Organizer
      Novel Quantum States in Condensed Matter 2022
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Tensor network approach to two-dimensional frustrated spin system2022

    • Author(s)
      Tsuyoshi Okubo
    • Organizer
      APCTP-IACS-SNBNCBS Workshop on Computational Methods for Emergent Quantum Matter: From Theoretical Concepts to Experimental Realization
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Tensor network approach to Kitaev spin liquid2022

    • Author(s)
      Tsuyoshi Okubo
    • Organizer
      The 15th Asia Pacific Physics Conference
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] PESS型テンソルネットワークによる拡張キタエフ模型の解析2022

    • Author(s)
      大久保毅
    • Organizer
      日本物理学会 2022年秋季大会
    • Related Report
      2022 Annual Research Report
  • [Presentation] テンソルネットワーク法の量子多体問題への適用と量子計算機への展開2022

    • Author(s)
      大久保毅
    • Organizer
      量子多体計算のフロンティア
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] キタエフ量子スピン液体の量子回路表現とその最適化2022

    • Author(s)
      大久保毅
    • Organizer
      日本物理学会第77回年次大会
    • Related Report
      2021 Research-status Report
  • [Presentation] スキルミオン結晶における位相シフト2022

    • Author(s)
      速水賢, 大久保毅, 求幸年
    • Organizer
      日本物理学会第77回年次大会
    • Related Report
      2021 Research-status Report
  • [Presentation] 量子物理とテンソルネットワーク2021

    • Author(s)
      大久保毅
    • Organizer
      第1回量子ソフトウェアワークショップ:テンソルネットワークと量子計算の展望
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] 拡張キタエフ模型における熱ホール伝導度の数値的研究2021

    • Author(s)
      大久保毅
    • Organizer
      キタエフ量子スピン液体研究の新展開
    • Related Report
      2021 Research-status Report
  • [Presentation] Tensor network approach to the magnetization of frustrated square lattice Heisenberg systems”2021

    • Author(s)
      Tsuyoshi Okubo
    • Organizer
      XXXII IUPAP Conference on Computational Physics (CCP2021),
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] Tensor network study of honeycomb lattice Kitaev model2021

    • Author(s)
      Tsuyoshi Okubo
    • Organizer
      Recent progress in theoretical physics based on quantum information theory
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] キタエフ量子スピン液体の熱ホール伝導度に対する非対角相互作用の効果2021

    • Author(s)
      大久保毅, 那須譲治, 三澤貴宏, 求幸年
    • Organizer
      日本物理学会第76回年次大会
    • Related Report
      2020 Research-status Report
  • [Presentation] 伝搬マイクロ波光子列クラスター状態の効率的な量子状態トモグラフィ2021

    • Author(s)
      砂田佳希, 河野信吾, Jesper Ilves, 杉山太香典, 鈴木泰成, 大久保毅, 玉手修平, 田渕豊, 中村泰信
    • Organizer
      日本物理学会第76回年次大会
    • Related Report
      2020 Research-status Report
  • [Presentation] Efficient tomography of microwave photonic cluster states2021

    • Author(s)
      Yoshiki Sunada, Shingo Kono, Jesper Ilves, Takanori Sugiyama, Yasunari Suzuki, Tsuyoshi Okubo, Yasunobu Nakamura
    • Organizer
      APS March Meeting 2021
    • Related Report
      2020 Research-status Report
  • [Presentation] Large spin fluctuation in the magnetization process of frustrated square lattice Heisenberg magnets2021

    • Author(s)
      Tsuyoshi Okubo
    • Organizer
      The International Workshop on Quantum Magnets in Extreme Conditions
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] A series of magnon crystals appearing under ultrahigh magnetic fields in a kagome antiferromagnet2021

    • Author(s)
      Ryutaro Okuma, Daisuke Nakamura, Tsuyoshi Okubo, Atsushi Miyake, Akira Matsuo, Koichi Kindo, Masashi Tokunaga, Naoki Kawashima, Shojiro Takeyama, Zenji Hiroi
    • Organizer
      APS March Meeting 2021
    • Related Report
      2020 Research-status Report
  • [Presentation] 密度行列のテンソルネットワーク表現による 有限温度キタエフ模型の解析2020

    • Author(s)
      大久保毅
    • Organizer
      物性研究所短期研究会 「量子多体計算と第一原理計算の新展開」
    • Related Report
      2020 Research-status Report
  • [Presentation] 二次元量子格子系テンソルネットワークソルバーパッケージ TeNeS2020

    • Author(s)
      本山裕一, 大久保毅, 森田悟史, 吉見一慶, 加藤岳生, 川島直輝
    • Organizer
      日本物理学会2020年秋季大会
    • Related Report
      2020 Research-status Report
  • [Presentation] テンソルネットワーク法による拡張キタエフ模型の有限温度物性の解析2020

    • Author(s)
      大久保毅
    • Organizer
      日本物理学会2020年秋季大会
    • Related Report
      2020 Research-status Report
  • [Presentation] テンソルネットワーク法による量子スピン系の基底状態計算2020

    • Author(s)
      大久保毅
    • Organizer
      物性研究所スパコン共同利用・CCMS合同研究会「計算物質科学の新展開2020」
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] Tensor network study on extended Kitaev models2020

    • Author(s)
      Tsuyoshi Okubo
    • Organizer
      The 33rd Annual CSP Workshop, Univerisity of Georgica
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 密度行列のテンソルネットワーク表示による有限温度キタエフ模型の解析2020

    • Author(s)
      大久保毅
    • Organizer
      日本物理学会第75回年次大会
    • Related Report
      2019 Research-status Report
  • [Presentation] テンソルネットワーク手法を用いたハニカム格子上のHeisenberg-Γ模型の基底状態探索2020

    • Author(s)
      金子隆威, 大久保毅, 川島直輝
    • Organizer
      日本物理学会第75回年次大会
    • Related Report
      2019 Research-status Report
  • [Presentation] ボンド重み付きテンソルくりこみ群2020

    • Author(s)
      足立大樹, 大久保毅, 藤堂眞治
    • Organizer
      日本物理学会第75回年次大会
    • Related Report
      2019 Research-status Report
  • [Presentation] Anisotropic tensor renormalization group and BTRG2019

    • Author(s)
      Tsuyoshi Okubo
    • Organizer
      Workshop on Tensor Network States: Algorithms and Applications (TNSAA2019-2020)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Large spin fluctuation in the magnetization process of frustrated square lattice Heisenberg model2019

    • Author(s)
      Tsuyoshi Okubo
    • Organizer
      Computational Approaches to Quantum Many-body Problems (CAQMP2019)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Tensor network approach to frustrated spin systems2019

    • Author(s)
      Tsuyoshi Okubo
    • Organizer
      Computational Approaches to Quantum Many-body Problems (CAQMP2019)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] テンソルネットワーク法の開発とキタエフスピン液体への適用2019

    • Author(s)
      大久保毅,金子隆威,Hyun-Yong Lee,山地洋平,川島直輝
    • Organizer
      ポスト「京」重点課題(7) 第5回シンポジウム
    • Related Report
      2019 Research-status Report
  • [Presentation] 無限系テンソルネットワーク状態の変分最適化とフラストレート磁性体への適用2019

    • Author(s)
      大久保毅
    • Organizer
      物性研究所スパコン共同利用・CCMS合同研究会「計算物質科学の新展開」
    • Related Report
      2019 Research-status Report
  • [Presentation] Searching for the Kitaev spin liquid by the tensor network approach2019

    • Author(s)
      金子 隆威、大久保 毅、H.-Y. Lee、山地 洋平、川島 直輝
    • Organizer
      物性研究所スパコン共同利用・CCMS合同研究会「計算物質科学の新展開」
    • Related Report
      2019 Research-status Report
  • [Presentation] Tensor Network Study of the Stability of the Kitaev Spin Liquid2019

    • Author(s)
      R. Kaneko, T. Okubo, H.-Y. Lee, Y. Yamaji, and N. Kawashima
    • Organizer
      International Conference on Strongly Correlated Electron Systems (SCES2019)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Study on Z2-vortex ordering by massively parallel Monte Carlo simulation2019

    • Author(s)
      T. Okubo and N. Kawashima
    • Organizer
      Frontiers of Statistical Physics (FSP2019)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Tensor network study of the Kitaev spin liquid2019

    • Author(s)
      R. Kaneko, T. Okubo, H.-Y. Lee, Y. Yamaji, and N. Kawashima,
    • Organizer
      Frontiers of Statistical Physics (FSP2019)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Tensor network approach to the Kitaev spin liquid2019

    • Author(s)
      R. Kaneko, T. Okubo, H.-Y. Lee, Y. Yamaji, and N. Kawashima
    • Organizer
      International Conference on Frontiers of Correlated Electron Sciences (FCES19)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] テンソルネットワーク法を用いた拡張Kitaev模型の基底状態探索2019

    • Author(s)
      金子 隆威、大久保 毅、H.-Y. Lee、山地 洋平、川島 直輝
    • Organizer
      第13回物性科学領域横断研究会
    • Related Report
      2019 Research-status Report
  • [Presentation] 無限系テンソルネットワークの変分最適化による拡張キタエフ模型の解析2019

    • Author(s)
      大久保毅
    • Organizer
      日本物理学会 2019年秋季大会
    • Related Report
      2019 Research-status Report
  • [Presentation] テンソルネットワーク手法を用いたKitaev-Γ模型のスピン液体の解析2019

    • Author(s)
      金子 隆威、大久保 毅、山地 洋平、川島 直輝
    • Organizer
      日本物理学会 2019年秋季大会
    • Related Report
      2019 Research-status Report
  • [Presentation] Kitaev Spin Liquids in a Compact Tensor Network Representation2019

    • Author(s)
      H.-Y. Lee, R. Kaneko, T. Okubo, and N. Kawashima,
    • Organizer
      日本物理学会 2019年秋季大会
    • Related Report
      2019 Research-status Report
  • [Presentation] 非等方的なテンソルくりこみ群2019

    • Author(s)
      足立大樹, 大久保毅, 藤堂眞治
    • Organizer
      日本物理学会 2019年秋季大会
    • Related Report
      2019 Research-status Report

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Published: 2019-04-18   Modified: 2024-01-30  

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