Numerical study of quantum frustrated systems by tensor network methods

• Project/Area Number: 23540450
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Kyoto University
• Principal Investigator: HARADA Kenji 京都大学, 情報学研究科, 助教 (80303882)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000); Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2011: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
• Keywords: テンソルネットワーク / フラストレーション / 量子スピン系 / MERA / スケーリング解析 / ベイズ推定 / トポロジカル秩序 / 非局所ユニタリー変換 / Valence bond solid / SU(N) JQモデル / SO(N) BLBQモデル / 量子モンテカルロ法 / 負符号問題 / 対称性で保護されたトポロジカル秩序 / エンタングルメント繰り込み / 反強磁性ハイゼンベルグモデル / シャストリー・サザーランド格子 / 変分法 / プラケットダイマー相 / 磁化プラトー / コード開発フレームワーク / 反強磁性ハイゼンベルグ / 三角格子 / スパイラル / 非整合

Research Abstract

We construct a new MERA tensor network based on entanglement renormalization for quantum triangular lattice models. We apply it to the ground state of an S = 1/2 antiferromagnetic Heisenberg model on a spatially anisotropic triangular lattice. Magnetic ground states are numerically confirmed in the weak anisotropic region. The magnetic structure is spiral with an incommensurate wave vector that is different from the classical one. We also develop a Bayesian method for the scaling analysis of critical systems, and a non-local unitary transformation for removing the negative sign problem in SO(N)bilinear-biquadratic chains. We also confirm the systematic shift of universality class to a weak first-order transition from large-scale quantum Monte Carlo calculations of two-dimensional SU(N) JQ models.

Research Products

• [Journal Article] Symmetry-protected topological order and negative-sign problem for SO(N) bilinear-biquadratic chains (2014)
  • Author(s): Kouchi Okunishi and Kenji Harada
  • Journal Title: Physical Review B Volume: 89 Issue: 13 Pages: 134422-134422
  • DOI: 10.1103/physrevb.89.134422
  • NAID: 120005666211
  • Peer Reviewed
• [Journal Article] Parallelized Quantum Monte Carlo Algorithm with Nonlocal Worm Updates (2014)
  • Author(s): Akiko Masaki, Takafumi Suzuki, Kenji Harada, Synge Todo, Naoki Kawashima
  • Journal Title: Phys. Rev. Lett Volume: 112 Issue: 14 Pages: 140603-140603
  • DOI: 10.1103/physrevlett.112.140603
  • Peer Reviewed / Open Access
• [Journal Article] Possibility of Deconfined Criticality in SU(N) Heisenberg Models at Small N (2013)
  • Author(s): Kenji Harada, Takafumi Suzuki, Tsuyoshi Okubo, Haruhiko Matsuo, Jie Lou, Hiroshi Watanabe, Synge Todo, Naoki Kawashima
  • Journal Title: Phys. Rev Volume: B88 Issue: 22
  • DOI: 10.1103/physrevb.88.220408
  • Peer Reviewed
• [Journal Article] 多体問題におけるテンソルネットワーク法 (2012)
  • Author(s): 原田健自
  • Journal Title: 京都大学数理解析研究所(RIMS) 研究集会 「次世代計算科学の基盤技術とその展開」 RIMS 研究集会報告書 Volume: No.1848 Pages: 83-92
  • URL: http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/1848.html
• [Journal Article] Numerical study of incommensurability of the spiral state on spin-1/2 spatially anisotropic triangular antiferromagnets using entanglement renormalization (2012)
  • Author(s): Kenji Harada
  • Journal Title: Physical Review B Volume: 86 Issue: 18 Pages: 184421-184421
  • DOI: 10.1103/physrevb.86.184421
  • NAID: 120005666213
  • Peer Reviewed
• [Journal Article] Bayesian inference in the scaling analysis of critical phenomena (2011)
  • Author(s): Kenji Harada
  • Journal Title: Physical Review E Volume: 84 Issue: 5 Pages: 56704-56704
  • DOI: 10.1103/physreve.84.056704
  • NAID: 120005666216
  • Peer Reviewed
• [Journal Article] Tensor Network Studies of Quantum Frustrated Magnets
  • Author(s): Kenji Harada
  • Journal Title: Proceedings of Strongly Correlated Electron Systems(SCES2013)
  • Peer Reviewed
• [Presentation] SU(N)ハイゼンベルクモデルで脱閉じ込め転移はあるのか? (2013)
  • Organizer: 物性研スパコン共同利用・CMSI合同研究会(第4回CMSI研究会)
  • Place of Presentation: 東京大学物性研究所
  • Year and Date: 2013-12-11
• [Presentation] Deconfined quantum criticality in SU(N) Heisenberg models : Finite size scaling analysis based on Bayesian inference (2013)
  • Organizer: Taipei Tensor Network Workshop 2013
  • Place of Presentation: National Taiwan University, Taipei (Taiwan)
  • Year and Date: 2013-12-04
• [Presentation] Tensor network studies of quantum frustrated magnets (2013)
  • Author(s): Kenji Harada
  • Organizer: Statistical Physics of Quantum Matter
  • Place of Presentation: Taipei, Taiwan
• [Presentation] Tensor network studies of quantum frustrated magnets (2013)
  • Author(s): Kenji Harada
  • Organizer: the International Conference on Strongly Correlated Electron Systems (SCES2013)
  • Place of Presentation: Tokyo, Japan
• [Presentation] 2次元 SU(N) J-Qモデルを用いた脱閉じ込め臨界現象の数値的研究 (2013)
  • Author(s): 原田健自
  • Organizer: 日本物理学会２０１３年秋季大会
  • Place of Presentation: 徳島市、徳島県
• [Presentation] Deconfined quantum criticality in SU(N) Heisenberg models: Finite size scaling analysis based on Bayesian inference (2013)
  • Author(s): Kenji Harada
  • Organizer: Taipei Tensor Network Workshop 2013
  • Place of Presentation: Taipei, Taiwan
  • Invited
• [Presentation] SU(N)ハイゼンベルクモデルで脱閉じ込め転移はあるのか？ (2013)
  • Author(s): 原田健自
  • Organizer: 物性研スパコン共同利用・CMSI 合同研究会（第４回 CMSI 研究会）
  • Place of Presentation: 柏市、千葉県
• [Presentation] 脱閉じ込め臨界現象のユニバーサリティ (2012)
  • Organizer: 第3回CMSI研究会~超並列計算が拓く新しい計算物質科学~
  • Place of Presentation: 自然科学研究機構 岡崎コンファレンスセンター
  • Year and Date: 2012-12-03
• [Presentation] Numerical study of quantum frustrated magnets using entanglement renormalization : spin-1/2 spatially anisotropic triangular antiferromagnets and Shastry-Sutherland model (2012)
  • Organizer: 基研研究会「量子スピン系の物理」
  • Place of Presentation: 京都大学基礎物理学研究所
  • Year and Date: 2012-11-13
• [Presentation] Numerical study of quantum frustrated magnets using entanglement renormalization (2012)
  • Organizer: International Workshop on Cooperative Quantum Dynamics and Its Control (CQDC'12)
  • Place of Presentation: Jeulich super computer center, Jeulich (Germany)
  • Year and Date: 2012-10-30
  • Invited
• [Presentation] 多体問題におけるテンソルネットワーク法 (2012)
  • Organizer: RIMS 研究集会「次世代計算科学の基盤技術とその展開」
  • Place of Presentation: 京都大学数理解析学研究所
  • Year and Date: 2012-10-24
  • Invited
• [Presentation] Numerical study of incommensurability of the spiral state on spin-1/2 spatially anisotropic triangular antiferromagnets using entanglement renormalization (2012)
  • Organizer: Conference on Computational Physics (CCP2012) for Physics, Chemistry, Biology, Engineering and related academic fields and industrial applications
  • Place of Presentation: Kobe (Japan)
  • Year and Date: 2012-10-15
• [Presentation] Bayesian Inference in the Scaling Analysis of Critical Phenomena (2012)
  • Organizer: International Workshop on Recent Developments of Studies on Phase Transitions 2012
  • Place of Presentation: University of Tokyo (Japan)
  • Year and Date: 2012-06-19
  • Invited
• [Presentation] テンソルネットワーク変分法 : 空間異方的な三角格子上の反強磁性ハイゼンベルグモデル (2012)
  • Organizer: CMSI 第1部会& CREST 主催「強相関系に対する計算科学手法とその応用」に関する研究会
  • Place of Presentation: 東京大学(本郷キャンパス)
  • Year and Date: 2012-01-28
• [Presentation] 空間異方性のある三角格子上の S=1/2 反強磁性ハイゼンベルグモデルの基底状態の磁気構造 (2012)
  • Author(s): 原田健自
  • Organizer: 特定領域「フラストレート系」最終成果報告会
  • Place of Presentation: 大阪大学
• [Presentation] エンタングルメント繰り込みを用いたフラストレーションのある量子スピン系の基底状態計算 (2012)
  • Author(s): 原田健自
  • Organizer: CMSI第1部会研究会「強相関系に対する計算科学手法とその応用」(招待講演)
  • Place of Presentation: 東京大学
• [Presentation] 三角格子上の格子モデルのためのエンタングルメント繰り込み (2011)
  • Organizer: 基研研究会「量子多体系のエンタングルメントとくりこみ群」
  • Place of Presentation: 京都大学基礎物理学研究所
  • Year and Date: 2011-12-16
• [Presentation] Magnetic Structure of Ground States in Spatially Anisotropic Triangular Antiferromagnets (2011)
  • Organizer: the 26th Nishinomiya-Yukawa Memorial International Workshop "Novel Quantum States in Condensed Matter 2011 (NQS2011)"
  • Place of Presentation: YITP, Kyoto University (Japan)
  • Year and Date: 2011-11-08
• [Presentation] Magnetic Structure of Ground States in Spatially Anisotropic Triangular Antiferromagnets (2011)
  • Author(s): Kenji Harada
  • Organizer: The 26th Nishinomiya-Yukawa Memorial International Workshop: Novel Quantum States in Condensed Matter 2011
  • Place of Presentation: YITP, Kyoto University
• [Presentation] Bayesian Inference in the Scaling Analysis of Critical Phenomena
  • Author(s): Kenji Harada
  • Organizer: International Workshop on Recent Developments of Studies on Phase Transitions 2012
  • Place of Presentation: Tokyo, Japan
• [Presentation] Tensor network method for fermionic system
  • Author(s): 原田 健自
  • Organizer: CMSI 第１部会「新物質新量子相の基礎科学」 夏の学校
  • Place of Presentation: 山形
• [Presentation] Numerical study of incommensurability of the spiral state on spin-1/2 spatially anisotropic triangular antiferromagnets using entanglement renormalization
  • Author(s): Kenji Harada
  • Organizer: Conference on Computational Physics (CCP2012) for Physics, Chemistry, Biology, Engineering and related academic fields and industrial applications
  • Place of Presentation: Kobe, Japan
• [Presentation] 多体問題におけるテンソルネットワーク法
  • Author(s): 原田 健自
  • Organizer: 京都大学 RIMS研究集会「次世代計算科学の基盤技術とその展開」
  • Place of Presentation: 京都
  • Invited
• [Presentation] Numerical study of quantum frustrated magnets using entanglement renormalization
  • Author(s): Kenji Harada
  • Organizer: International Workshop on Cooperative Quantum Dynamics and Its Control (CQDC'12)
  • Place of Presentation: Julich, Germany
  • Invited
• [Presentation] テンソルネットワーク変分法の開発
  • Author(s): 原田 健自
  • Organizer: 物性研究所共同利用スーパーコンピュータ・計算物質科学研究センター(CCMS)・元素戦略プロジェクト 合同研究会「計算物性物理学の新展開」
  • Place of Presentation: 東京
• [Remarks]
  • URL: http://www-fcs.acs.i.kyoto-u.ac.jp/~harada/