Energy-scale controlling of quantum many-body systems and entanglemet renormalization

• Project/Area Number: 17H02931
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Niigata University
• Principal Investigator: Okunishi Kouichi 新潟大学, 自然科学系, 准教授 (30332646)
• Co-Investigator(Kenkyū-buntansha): 引原 俊哉 群馬大学, 大学院理工学府, 准教授 (00373358)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Project Status: Completed (Fiscal Year 2020)
• Budget Amount: ¥18,720,000 (Direct Cost: ¥14,400,000、Indirect Cost: ¥4,320,000); Fiscal Year 2020: ¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000); Fiscal Year 2019: ¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000); Fiscal Year 2018: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000); Fiscal Year 2017: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
• Keywords: テンソルネットワーク / エンタングルメント / くりこみ群 / 角転送行列 / 量子多体系 / ランダムシングレット / ランダムスピン系 / ウンルー効果 / 数値くりこみ群 / 共形場理論 / サイン2乗変形 / 物性基礎論 / 計算物理

Outline of Final Research Achievements

Analyzing the mathematical structure of the entanglement Hamiltonian for the quantum spin systems, we proposed the lattice Unruh effect, which is a quantum spin system version of the Unruh effect for the quantum gravity. We also clarified phase transitions of regular polygon models and 6-state clock models, using high precision corner-transfer-matrix renormalization groups combined with the CFT analysis of the entanglement Hamiltonian. In addition, we have formulated new tensor network algorithms for random quantum spin systems.

Academic Significance and Societal Importance of the Research Achievements

これまであまり注目されてこなかった量子多体系のエンタングルメントハミルトニアンの空間非一様性の背後にある数理構造の解析を通じて、格子Unruh効果という、理論的にも実験的にも大変興味深い現象を提案できた。これにより、現実的な物性系で疑似的量子重力現象の検証が可能になり、物性にとどまらない大きな波及効果が期待される。また、テンソルネットワーク法の背景の理解が深まったことで、臨界現象解析の信頼性が大きく向上しただけなく、ランダム系に対するアルゴリズムの性能向上も達成できた。今後の物性系の定量解析にも大いに役立つと期待される。

Research Products

• [Int'l Joint Research] スロバキア科学アカデミー(スロバキア)
• [Int'l Joint Research] スロバキア科学アカデミー(スロバキア)
• [Int'l Joint Research] スロバキア科学アカデミー(スロバキア)
• [Journal Article] Magnetoelastic study on the frustrated quasi-one-dimensional spin-12 magnet LiCuVO4 (2021)
  • Author(s): A. Miyata, T. Hikihara, S. Furukawa, R. K. Kremer, S. Zherlitsyn, J. Wosnitza
  • Journal Title: Physical Review B Volume: 103 Issue: 1 Pages: 1-8
  • DOI: 10.1103/physrevb.103.014411
  • 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 model (2020)
  • 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
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Corner transfer matrix renormalization group analysis of the two-dimensional dodecahedron model (2020)
  • 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
  • Peer Reviewed
• [Journal Article] Tensor-network strong-disorder renormalization groups for random quantum spin systems in two dimensions (2020)
  • Author(s): Kouichi Seki, Toshiya Hikihara, and Kouichi Okunishi
  • Journal Title: Physical Review B Volume: 102 Issue: 14 Pages: 144439-144439
  • DOI: 10.1103/physrevb.102.144439
  • Peer Reviewed
• [Journal Article] Unconventional magnetic excitations and spin dynamics of exotic quantum spin systems BaCo_2V_2O_8 and Ba_3CuSb_2O_9 (2020)
  • Author(s): Han Yibo、Kimura Shojiro、Okunishi Kouichi、Hagiwara Masayuki
  • Journal Title: Applied Magnetic Resonance Volume: 2020 Issue: 4 Pages: 1-14
  • DOI: 10.1007/s00723-020-01296-w
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Lattice Unruh Effect and World-line Entanglement for the XXZ Chain (2019)
  • Author(s): Okunishi Kouichi、Seki Kouichi
  • Journal Title: Journal of the Physical Society of Japan Volume: 88 Issue: 11 Pages: 114002-114002
  • DOI: 10.7566/jpsj.88.114002
  • NAID: 130008156470
  • Peer Reviewed / Open Access
• [Journal Article] Magnetic Properties of One- and Two-Dimensional Functional Materials: Oxygen Molecules Encapsulated in Single-Walled Carbon Nanotubes and Copper Ions Embedded into Phthalocyanine Sheets (2019)
  • Author(s): M. Hagiwara, T. Kida, K. Matsuda, H. Kyakuno, Y. Mniwa, Z. Honda, Y. Sakaguchi, M. Tashiro, M. Sakai, T. Fukuda, N. Kamata and K. Okunishi
  • Journal Title: Open Chemistry Journal Volume: 6 Issue: 1 Pages: 27-33
  • DOI: 10.2174/1874842201906010027
  • Peer Reviewed / Open Access
• [Journal Article] Quantum phase transitions beyond Landau-Ginzburg theory in one-dimensional space revisited (2019)
  • Author(s): Mudry Christopher、Furusaki Akira、Morimoto Takahiro、Hikihara Toshiya
  • Journal Title: Physical Review B Volume: 99 Issue: 20 Pages: 205153-205153
  • DOI: 10.1103/physrevb.99.205153
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Spin nematics in frustrated spin-dimer systems with bilayer structure (2019)
  • Author(s): Hikihara Toshiya、Misawa Takahiro、Momoi Tsutomu
  • Journal Title: Physical Review B Volume: 100 Issue: 21 Pages: 214414-214414
  • DOI: 10.1103/physrevb.100.214414
  • Peer Reviewed
• [Journal Article] Snapshot Spectra in the World-Line Quantum Monte Carlo for One-Dimensional Quantum Spin Systems (2019)
  • Author(s): Seki Kouichi、Okunishi Kouichi
  • Journal Title: Journal of the Physical Society of Japan Volume: 88 Issue: 2 Pages: 024003-024003
  • DOI: 10.7566/jpsj.88.024003
  • NAID: 210000135087
  • Peer Reviewed
• [Journal Article] A low-energy effective model for the S=1/2 Kagome-triangular-strip Heisenberg model (2018)
  • Author(s): Okunishi Kouichi、Onozato Yoshitaka、Seki Kouichi
  • Journal Title: AIP Advances Volume: 8 Issue: 10 Pages: 101401-101401
  • DOI: 10.1063/1.5042702
  • Peer Reviewed
• [Journal Article] Ground-State Phase Diagram of an Anisotropic S = 1/2 Ladder with Different Leg Interactions (2018)
  • Author(s): Tonegawa Takashi、Hikihara Toshiya、Okamoto Kiyomi、Furuya Shunsuke C.、Sakai Toru
  • Journal Title: Journal of the Physical Society of Japan Volume: 87 Issue: 10 Pages: 104002-104002
  • DOI: 10.7566/jpsj.87.104002
  • NAID: 210000134973
  • Peer Reviewed / Open Access
• [Journal Article] Phase Transitions for Cuboc Orders in Stacked Kagome Heisenberg Systems (2018)
  • Author(s): Seki Kouichi、Okunishi Kouichi
  • Journal Title: Journal of the Physical Society of Japan Volume: 87 Issue: 2 Pages: 023001-023001
  • DOI: 10.7566/jpsj.87.023001
  • NAID: 210000134681
  • Peer Reviewed / Open Access
• [Journal Article] Spin-Wave Analysis for Kagome-Triangular Spin System and Coupled Spin Tubes: Low-Energy Excitation for the Cuboc Order (2017)
  • Author(s): Ochiai Masahiro、Seki Kouichi、Okunishi Kouichi
  • Journal Title: Journal of the Physical Society of Japan Volume: 86 Issue: 11 Pages: 114701-114701
  • DOI: 10.7566/jpsj.86.114701
  • NAID: 210000134583
  • Peer Reviewed
• [Journal Article] Critical behavior of the two-dimensional icosahedron model (2017)
  • 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
  • Peer Reviewed / Int'l Joint Research
• [Presentation] "Lattice Unruh effect and world-line entanglement for the XXZ chain" (2021)
  • Author(s): Kouichi Okunishi
  • Organizer: Recent progress in theoretical physics based on quantum information theory
  • Int'l Joint Research / Invited
• [Presentation] ランダムJ1-J2スピン鎖の基底状態相図と低温特性 (2021)
  • Author(s): 上松和樹
  • Organizer: 日本物理学会年次大会
• [Presentation] ランダムJ1-J2スピン鎖におけるフラストレート・ランダムシングレット状態 (2021)
  • Author(s): 引原俊哉
  • Organizer: 日本物理学会年次大会
• [Presentation] 擬一次元S=1/2フラストレート強磁性体LiCuVO4の磁場中磁歪測定 (2021)
  • Author(s): 引原俊哉
  • Organizer: 第15回量子スピン系研究会
• [Presentation] XXZ鎖における格子Unruh効果と世界線のエンタングルメント (2020)
  • Author(s): 奥西巧一
  • Organizer: 日本物理学会秋季大会
• [Presentation] カゴメ-三角格子における磁場下でのスキルミオン相 (2020)
  • Author(s): 関孝一
  • Organizer: 日本物理学会秋季大会
• [Presentation] AKLT鎖における角度時間相関関数 (2020)
  • Author(s): 中島康太郎
  • Organizer: 日本物理学会秋季大会
• [Presentation] 穴空き2次元イジング模型のエンタングルメントのCTMRG法による解析 (2020)
  • Author(s): 山本龍人
  • Organizer: 日本物理学会秋季大会
• [Presentation] Tree Tensor Network を用いた量子系の最適表現I (2020)
  • Author(s): 西野友年
  • Organizer: 日本物理学会秋季大会
• [Presentation] エンタングルメント分割と樹状テンソルネットワークの相互情報量最適化原理 (2019)
  • Author(s): 奥西巧一、上田宏、西野友年
  • Organizer: 日本物理学会秋期大会
• [Presentation] 実空間繰り込み群法の改良と二次元ランダム量子スピン系への適用 (2019)
  • Author(s): 関孝一、引原俊哉、奥西巧一
  • Organizer: 日本物理学会秋季大会
• [Presentation] XXZ鎖における格子Unruh効果と世界線エンタングルメント (2019)
  • Author(s): 奥西巧一
  • Organizer: サイン2乗変形（SSD）とその周辺2019
• [Presentation] Corner transfer matrix and lattice Unruh effect for the XXZ chain (2019)
  • Author(s): 奥西巧一
  • Organizer: Tensor Network States: Algorithms and Applications 2019-2020
  • Int'l Joint Research / Invited
• [Presentation] Numerical strong-disorder renormalization group for two-dimensional random quantum spin systems (2019)
  • Author(s): 関孝一、引原俊哉、奥西巧一
  • Organizer: Tensor Network States: Algorithms and Applications 2019-2020
  • Int'l Joint Research
• [Presentation] spin-1/2 J1-J2 XYZ鎖における非GL的量子臨界相転移 (2019)
  • Author(s): 引原俊哉, Christopher Mudry, 古崎昭, 森本高裕
  • Organizer: 日本物理学会秋期大会
• [Presentation] フラストレート・スピンダイマー系におけるスピンネマティック秩序状態の多変数変分モンテカルロ法による解析 (2019)
  • Author(s): 三澤貴宏, 引原俊哉, 桃井勉
  • Organizer: 日本物理学会秋期大会
• [Presentation] 二次元ランダム量子スピン系に対する実空間くりこみ群法の改良と性能評価 (2019)
  • Author(s): 関孝一
  • Organizer: 日本物理学会年次大会（九州大学）
• [Presentation] 1次元量子系のエンタングルメントスペクトルとCFTのメビウス量子化 (2019)
  • Author(s): 奥西巧一
  • Organizer: 日本物理学会年次大会（九州大学）
• [Presentation] A low-energy effective model for the S=1/2 Kagome-triangular-strip Heisenberg model (2018)
  • Author(s): Kouichi Okunishi
  • Organizer: International Conference of Magnetism 2018
  • Int'l Joint Research
• [Presentation] Ground States in an Anisotropic S=1/2 Ladder with Different Leg Interactions (2018)
  • Author(s): Toshiya Hikihara
  • Organizer: International Conference on Magnetism 2018
  • Int'l Joint Research
• [Presentation] Scaling analysis of snapshot spectra in the world-line quantum MonteCarlo for one-dimensional quantum spin systems (2018)
  • Author(s): Kouichi Seki
  • Organizer: Tensor Network States:Algorithms and Applications
  • Int'l Joint Research
• [Presentation] MonteCarlo studies of phase transitions for cuboc orders in stacked kagome Heisenberg systems (2018)
  • Author(s): Kouichi Seki
  • Organizer: 3rd international symposium on research and education of computational science
  • Int'l Joint Research
• [Presentation] 二次元ランダム量子スピン系解析のための実空間繰り込み群法の改良 (2018)
  • Author(s): 引原俊哉
  • Organizer: 京都大学基礎物理研究所研究会
• [Presentation] 積層カゴメ格子における立体秩序Cubocの研究 (2018)
  • Author(s): 関孝一
  • Organizer: 京都大学基礎物理研究所研究会
• [Presentation] 連続スピン系における弱い一時相転移の検出 (2018)
  • Author(s): 関孝一
  • Organizer: 日本物理学会秋季大会（同志社大学）
• [Presentation] 量子モンテカルロ法を用いたランダム量子スピン系の実空間くりこみ群法の性能評価 (2018)
  • Author(s): 関孝一
  • Organizer: 日本物理学会秋季大会（同志社大学）
• [Presentation] 共形場理論のメビウス量子化とエンタングルメント (2018)
  • Author(s): 奥西巧一
  • Organizer: 日本物理学会秋季大会（同志社大学）
• [Presentation] サイン２乗変形と運動量 (2018)
  • Author(s): 奥西巧一
  • Organizer: 日本物理学会第73回年次大会
• [Presentation] カゴメ 三角ストリップ模型の有効模型 (2018)
  • Author(s): 小野里佳孝, 奥西巧一, 関孝一
  • Organizer: 日本物理学会第73回年次大会
• [Presentation] カゴメ 三角格子ストリップ上のスピン模型の磁化過程 (2017)
  • Author(s): 小野里佳孝, 奥西巧一, 関孝一
  • Organizer: 日本物理学会第2017年秋期大会
• [Presentation] 離散化された古典ハイゼンベルグ模型に現れる相転移 (2017)
  • Author(s): 上田宏, 奥西巧一, Roman Krcmar, Andrej Gendiar, 柚木清司, 西野友年
  • Organizer: 日本物理学会第2017年秋期大会
• [Presentation] SSD and other energy deformations (2017)
  • Author(s): Toshiya Hikihara
  • Organizer: Workshop on Sine square deformation and related topics
• [Presentation] Sine-square deformation and Mobius quantization of 2D CFTs (2017)
  • Author(s): Kouichi Okunishi
  • Organizer: Workshop on Sine square deformation and related topics
• [Presentation] S=1/2反強磁性ハイゼンベルグ鎖におけるダイマー相関振幅とボンド交替による励起ギャップ (2017)
  • Author(s): 引原俊哉, 古崎昭, Sergei Lukyanov
  • Organizer: 日本物理学会2017年秋季大会
• [Presentation] Spin-nematic ordering in two- and three-dimensional frustrated quantum magnets composed of spin dimers (2017)
  • Author(s): Toshiya Hikihara, Tsutomu Momoi
  • Organizer: Junjiro Kanamori Memorial International Symposium
  • Int'l Joint Research