Study on Phase Transitions and Dynamics of Spin System with Long-range Interactions

• Project/Area Number: 20540364
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: The University of Tokyo
• Principal Investigator: TODO Synge The University of Tokyo, 大学院・工学系研究科, 講師 (10291337)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 長距離相互作用 / モンテカルロ法 / 詳細釣り合い条件 / 量子モンテカルロ法 / エンタングルメントエントロピー / 臨界現象 / 並列計算 / 負符号問題 / 磁気双極子相互作用 / 相転移 / ランダムネス / ダイナミクス / スピンアイス

Research Abstract

It has long been very difficult to simulate spin systems with long-range interactions since the number of interactions increases proportional to the square of the number of spins. We have developed an Order-N Monte Carlo method for generic long-range interacting system. We have also developed a versatile algorithm, which minimizes the rejection rate in Monte Carlo method. In addition, we have revealed the low-temperature phase of the spin-ice and the effect of quantum phonon in spin-Peierls system, and proposed methods to measure the entanglement entropy and local Z_2 Berry phase.

Research Products

• [Journal Article] 詳細つりあいを満たさないモンテカルロ法 (2011)
  • Author(s): 諏訪秀麿,藤堂眞治
  • Journal Title: 日本物理学会誌 66 Pages: 370-370
  • Peer Reviewed
• [Journal Article] The ALPS project release 2.0 : Open source software for strongly correlated systems (2011)
  • Author(s): B.Bauer, L.D.Carr, A.Feiguin, J.Freire, S.Fuchs, L.Gamper, J.Gukelberger, E.Gull, S.Guertler, A.Hehn, R.Igarashi, S.V.Isakov, D.Koop, P.N.Ma, P.Mates, H.Matsuo, O.Parcollet, G.Pawlowski, J.D.Picon, L.Pollet, E.Santos, V.W.Scarola, U.Schollwock, C.Silva, B.Surer, S.Todo, S.Trebst, M.Troyer, M.L.Wall, P.Werner, S.Wessel
  • Journal Title: J.Stat.Mech. Pages: 5001-5001
  • Peer Reviewed
• [Journal Article] Markov Chain Monte Carlo Method without Detailed Balance (2011)
  • Author(s): H.Suwa, S.Todo
  • Journal Title: Phys.Rev.Lett. 105 Pages: 120603-120603
  • Peer Reviewed
• [Journal Article] 詳細つりあいを満たさないモンテカルロ法 (2011)
  • Author(s): 諏訪秀麿
  • Journal Title: 日本物理学会誌 Volume: 66(印刷中(掲載確定))
  • Peer Reviewed
• [Journal Article] The ALPS project release 2.0 : Open source software for strongly correlated systems (2011)
  • Author(s): B.Bauer
  • Journal Title: JSTAT Volume: (印刷中(掲載確定))
  • Peer Reviewed
• [Journal Article] Orbital ordering in eg orbital systems : Ground states and thermodynamics of the 120 degree model (2010)
  • Author(s): A.van Rynbach, S.Todo, S.Trebst
  • Journal Title: Phys.Rev.Lett. 105 Pages: 146402-146402
  • Peer Reviewed
• [Journal Article] Markov Chain Monte Carlo Method without Detailed Balance (2010)
  • Author(s): H.Suwa
  • Journal Title: Phys.Rev.Lett. Volume: 105 Pages: 120603-120603
  • Peer Reviewed
• [Journal Article] Orbital ordering in eg orbital systems : Ground states and thermodynamics of the 120 degree model (2010)
  • Author(s): A.van Rynbach
  • Journal Title: Phys.Rev.Lett. Volume: 105 Pages: 146402-146402
  • Peer Reviewed
• [Journal Article] Order-N Cluster Monte Carlo Method for Spin Systems with Long-range Interactions (2009)
  • Author(s): K.Fukui, S.Todo
  • Journal Title: J.Comp.Phys. 228 Pages: 2629-2629
  • Peer Reviewed
• [Journal Article] Successive phase transitions at finite temperatures of the supersolid in the three-dimensional extended Bose-Hubbard model (2009)
  • Author(s): K.Yamamoto, S.Todo, S.Miyashita
  • Journal Title: Phys.Rev.B 79 Pages: 94503-94503
  • Peer Reviewed
• [Journal Article] High-Field Magnetism of the Spin-Ladder Material Na_2Fe_2(C_2O_4)_3(H_2O)_2 (2009)
  • Author(s): H.Yamaguchi, S.Kimura, Z.Honda, K.Okunishi, S.Todo, K.Kindo, M.Hagiwara
  • Journal Title: J.Phys.Soc.Jpn. 78 Pages: 124701-124701
  • Peer Reviewed
• [Journal Article] High-Field Magnetism of the Spin-Ladder Material Na_2Fe_2(C_2O_4)_3(H_2O)_2 (2009)
  • Author(s): H.Yamaguchi
  • Journal Title: J.Phys.Soc.Jpn. 78 Pages: 124701-124701
  • Peer Reviewed
• [Journal Article] Order-N Cluster Monte Carlo Method for Spin Systems with Long-range Interactions (2009)
  • Author(s): K. Fukui
  • Journal Title: J. Comp. Phys. 228 Pages: 2629-2642
  • Peer Reviewed
• [Journal Article] Successive phase transitions at finite temperatures toward the supersolid state in a three-dimensional extended Bose-Hubbard model (2009)
  • Author(s): K. Yamamoto
  • Journal Title: Phys. Rev. B 79
  • Peer Reviewed
• [Journal Article] Green's function theory for spin-1/2 ferromagnets with an easy-plane exchange anisotropy (2008)
  • Author(s): D.Yamamoto, S.Todo, S.Kurihara
  • Journal Title: Phys.Rev.B 78 Pages: 24440-24440
  • Peer Reviewed
• [Journal Article] Improved chain mean-field theory for quasi-one-dimensional quantum magnets (2008)
  • Author(s): 藤堂眞治, A.Shibasaki
  • Journal Title: Phys.Rev.B 78 Pages: 224411-224411
  • Peer Reviewed
• [Journal Article] Green's function theory for spin-1/2 ferromagnets with an easy-plane exchange anisotorpy (2008)
  • Author(s): D. Yamamoto
  • Journal Title: Phys. Rev. B 78
  • Peer Reviewed
• [Journal Article] Improved chain mean-field theory for quasi-one dimensional quantum magnets (2008)
  • Author(s): S. Todo
  • Journal Title: Phys. Rev. B 78
  • Peer Reviewed
• [Presentation] 大規模並列量子モンテカルロ法ALPS/looper,次世代ナノ統合シミュレーションソフトウェアの研究開発 (2011)
  • Author(s): 藤堂眞治
  • Organizer: 第5回公開シンポジウム
  • Place of Presentation: 神戸
  • Year and Date: 2011-02-22
• [Presentation] 大規模並列量子モンテカルロ法ALPS/looper (2011)
  • Author(s): 藤堂眞治
  • Organizer: 次世代ナノ統合シミュレーションソフトウェアの研究開発 第5回公開シンポジウム
  • Place of Presentation: 神戸
  • Year and Date: 2011-02-22
• [Presentation] Markov chain Monte Carlo without Detailed Balance (2010)
  • Author(s): 藤堂眞治
  • Organizer: APPC11 The 11th Asia Pacific Physics Conference
  • Place of Presentation: Shanghai, CHINA
  • Year and Date: 2010-11-18
• [Presentation] Quantum Monte Carlo Measurement of Entanglement Entropy (2010)
  • Author(s): 藤堂眞治
  • Organizer: NTTCM2010 Japan-Switzerland Joint Workshop New Trends in Theory of Correlated Materials
  • Place of Presentation: Chiba
  • Year and Date: 2010-09-08
• [Presentation] Markov Chain Monte Carlo without Detailed Balance and Bounce-free Worm Algorithm (2010)
  • Author(s): H.Suwa, S.Todo
  • Organizer: Monte Carlo Algorithms in Statistical Physics
  • Place of Presentation: Melbourne, AUSTRALIA
  • Year and Date: 2010-07-27
• [Presentation] Quantum Monte Carlo method for particle number non-conserved systems and application to spin-Pelerls systems (2010)
  • Author(s): H.Suwa, S.Todo
  • Organizer: STATPHYS24 XXIV IUPAP International Conference on Statistical Physics
  • Place of Presentation: Cairns, AUSTRALIA
  • Year and Date: 2010-07-22
• [Presentation] Order-N Monte Carlo Method for Long-range Interacting Systems and its Applications (2010)
  • Author(s): 藤堂眞治
  • Organizer: STATPHYS24 XXIV IUPAP International Conference on Statistical Physics
  • Place of Presentation: Cairns, AUSTRALIA
  • Year and Date: 2010-07-20
• [Presentation] スピンパイエルス系における非磁性不純物効果2 (2010)
  • Author(s): 諏訪秀麿,藤堂眞治
  • Organizer: 日本物理学会第65回年次大会
  • Place of Presentation: 岡山
  • Year and Date: 2010-03-22
• [Presentation] 量子モンテカルロ法による量子クロック模型のスティッフネスの計算 (2010)
  • Author(s): 松尾春彦,藤堂眞治
  • Organizer: 日本物理学会第65回年次大会
  • Place of Presentation: 岡山
  • Year and Date: 2010-03-22
• [Presentation] フラストレーションした量子反強磁性ハイゼンベルグ模型のモンテカルロ法 (2010)
  • Author(s): 本山裕一,藤堂眞治
  • Organizer: 日本物理学会第65回年次大会
  • Place of Presentation: 岡山
  • Year and Date: 2010-03-22
• [Presentation] Wang-Landau法によるエンタングルメントエントロピーの計算 (2010)
  • Author(s): 藤堂眞治
  • Organizer: 日本物理学会第65回年次大会
  • Place of Presentation: 岡山
  • Year and Date: 2010-03-22
• [Presentation] 量子モンテカルロ法の大規模並列化 (2010)
  • Author(s): 藤堂眞治
  • Organizer: 次世代ナノ情報機能・材料分野公開研究会「新物質とエネルギー」
  • Place of Presentation: 東京
  • Year and Date: 2010-03-11
• [Presentation] QMC Challenges for Spin/bosonic Lattice Models (2009)
  • Author(s): 藤堂眞治
  • Organizer: The Next Generation of Quantum Simulations
  • Place of Presentation: Moorea
  • Year and Date: 2009-05-03
• [Presentation] QMC Challenges for Spin/bosonic Lattice Models (2009)
  • Author(s): 藤堂眞治
  • Organizer: The Next Generation of Quantum Simulations
  • Place of Presentation: Moorea,フランス
  • Year and Date: 2009-05-03
• [Presentation] ダイポールスピンアイスの長距離秩序相 (2009)
  • Author(s): 藤堂眞治
  • Organizer: 日本物理学会第64回年次大会
  • Place of Presentation: 東京
  • Year and Date: 2009-03-30
• [Presentation] 量子モンテカルロ法による古典2次元クロック模型の解析 (2009)
  • Author(s): 松尾春彦,藤堂眞治
  • Organizer: 日本物理学会第64回年次大会
  • Place of Presentation: 東京
  • Year and Date: 2009-03-30
• [Presentation] 量子数の保存しない系に対する量子モンテカルロ法とスピンパイエルス系への応用 (2009)
  • Author(s): 諏訪秀麿,藤堂眞治
  • Organizer: 日本物理学会第64回年次大会
  • Place of Presentation: 東京
  • Year and Date: 2009-03-30
• [Presentation] 量子モンテカルロシミュレーションによるエンタングルメントエントロピーの計測 (2009)
  • Author(s): 金井龍一,藤堂眞治
  • Organizer: 日本物理学会第64回年次大会
  • Place of Presentation: 東京
  • Year and Date: 2009-03-30
• [Presentation] Low-energy Properties of Frustrated Ising Magnets with Competing Exchange and Dipole Interactions (2009)
  • Author(s): 藤堂眞治
  • Organizer: Supercomputing in Solid State Physics 2009
  • Place of Presentation: 柏
  • Year and Date: 2009-02-18
• [Presentation] Low-energy Properties of Frustrated Ising Magnets with Competing Echange and Dipole Interacti (2009)
  • Author(s): S. Todo
  • Organizer: Supercomputing in Solid State Physics 2009
  • Place of Presentation: 柏
  • Year and Date: 2009-02-18
• [Presentation] Order-N Monte Carlo Algorithm for Long-range Interacting Spin Systems : Application to Dipoler Spin Ice (2008)
  • Author(s): 藤堂眞治
  • Organizer: International Workshop on Novel Aspects of Phase Transitions with Long-range Interactions
  • Place of Presentation: 東京
  • Year and Date: 2008-10-28
• [Presentation] Order-N Monte Carlo Algorithm for Long-range Interacting Spin Systems: Application to Dipoler Spin Ice (2008)
  • Author(s): S. Todo
  • Organizer: International Workshop on Novel Aspects of Phase Transitions with Long-range Interactions
  • Place of Presentation: 東京
  • Year and Date: 2008-10-28
• [Presentation] 長距離相互作用を持つスピン系の拡張アンサンブルモンテカルロシミュレーション (2008)
  • Author(s): 藤堂眞治
  • Organizer: 日本物理学会 2008年秋季大会
  • Place of Presentation: 盛岡
  • Year and Date: 2008-09-22
• [Presentation] スピンパイエルス系における格子の分散関係と次元性の効果 (2008)
  • Author(s): 諏訪秀麿,藤堂眞治
  • Organizer: 日本物理学会 2008年秋季大会
  • Place of Presentation: 盛岡
  • Year and Date: 2008-09-22
• [Presentation] 長距離相互作用を持つスピン系の拡張アンサンブルモンテカルロシミュレーシヨシ (2008)
  • Author(s): 藤堂眞治
  • Organizer: 日本物理学会2008年秋季大会
  • Place of Presentation: 盛岡
  • Year and Date: 2008-09-22
• [Presentation] スピンパイエルス系における格子の分散関係と次元性の効果 (2008)
  • Author(s): 諏訪秀麿
  • Organizer: 日本物理学会2008年秋季大会
  • Place of Presentation: 盛岡
  • Year and Date: 2008-09-22
• [Presentation] Large-scale parallel quantum Monte Carlo simulation of low-dimensional quantum magnets (2008)
  • Author(s): 藤堂眞治
  • Organizer: 1st International Conference of the Grand Challenge to Next-Generation Integrated Nanoscience
  • Place of Presentation: 東京
  • Year and Date: 2008-06-06
• [Presentation] Large-scale parallel quantum Monte Carlo simulation of low dimensional quantum magnets (2008)
  • Author(s): S. Todo
  • Organizer: 1st International Conference of the Grand Challenge to Next-Generation Integrated Nanoscience
  • Place of Presentation: 東京
  • Year and Date: 2008-06-06
• [Remarks] ホームページ等
  • URL: http://todo.ap.t.u-tokyo.ac.jp
• [Remarks]
  • URL: http://alps.comp-phys.org