Geometric Approach to Markov Chain Monte Carlo

• Project/Area Number: 23540438
• 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: The University of Tokyo
• Principal Investigator: TODO Synge 東京大学, 理学(系)研究科(研究院), 准教授 (10291337)
• 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: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2011: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
• Keywords: 計算物理 / モンテカルロ法 / アルゴリズム / 磁性 / 統計物理 / 物性基礎論 / 統計力学 / 物性理論

Research Abstract

We have applied geometric approaches, such as the landfilling method, to the Markov chain Monte Carlo method, which is one of the most powerful method to strongly correlated many-body systems, and found a generic method that drastically accelerates the convergence of Markov chain. We have also developed a precise estimator of energy gap, quantum Monte Carlo level spectroscopy, method for calculating the local Z_N Berry phase, new finite size scaling method for systems with strong spatial anisotropy. In addition, we have developed and made public the BCL library - the generic library for the landfilling method, and the Worms Package - the quantum Monte Carlo application based on the BCL library.

Research Products

• [Journal Article] Path-Integral Monte Carlo for the Gauge-Fixed Berry Connection and the Local Z_2 Berry Phase (2014)
  • Author(s): Yuichi Motoyama, Synge Todo
  • Journal Title: JPS Conf. Proc Volume: 1 Pages: 12130-12130
  • DOI: 10.7566/jpscp.1.012130
  • Peer Reviewed
• [Journal Article] Numerical Analysis of Quantum Phase Transitions with Dynamic Control of Anisotropy (2014)
  • Author(s): Shinya Yasuda, Synge Todo
  • Journal Title: JPS Conf. Proc Volume: 1 Pages: 12127-12127
  • DOI: 10.7566/jpscp.1.012127
  • 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] 詳細つりあいを満たさないマルコフ連鎖モンテカルロ法とその一般化 (2013)
  • Author(s): 諏訪秀麿, 藤堂眞治
  • Journal Title: 数理解析研究所 講究録 Volume: 1848 Pages: 93-107
  • URL: http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/1848.html
• [Journal Article] Geometric Allocation Approaches in Markov Chain Monte Carlo (2013)
  • Author(s): Synge Todo, Hidemaro Suwa
  • Journal Title: J. Phys. : Conf. Ser Volume: 473 Pages: 12013-12013
  • DOI: 10.1088/1742-6596/473/1/012013
  • Peer Reviewed
• [Journal Article] Monte Carlo simulation with aspect ratio optimization: Anomalous anisotropic scaling in dimerized antiferromagnet (2013)
  • Author(s): Shinya Yasuda, Synge Todo
  • Journal Title: Phys. Rev. E Volume: 88 Issue: 6
  • DOI: 10.1103/physreve.88.061301
  • Peer Reviewed
• [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] Long-Range Order of the Three-Sublattice Structure in the S=1 Heisenberg Antiferromagnet on a Spatially Anisotropic Triangular Lattice (2013)
  • Author(s): H. Nakano
  • Journal Title: Journal of the Physical Society of Japan Volume: 82 Issue: 4 Pages: 43715-43715
  • DOI: 10.7566/jpsj.82.043715
  • NAID: 210000132502
  • Peer Reviewed
• [Journal Article] Path-integral Monte Carlo method for the local Z2 Berry phase (2013)
  • Author(s): Yuichi Motoyama, Synge Todo
  • Journal Title: Phys. Rev Volume: E87 Issue: 2
  • DOI: 10.1103/physreve.87.021301
  • Peer Reviewed
• [Journal Article] Geometric allocation approach for transition kernel of Markov chain (2012)
  • Author(s): Hidemaro Suwa, Synge Todo
  • Journal Title: Monte Carlo Methods and Applications (proceedings of Eighth IMACS Seminar on Monte Carlo Methods), ed. K. K. Sabelfeld, I. Dimov Pages: 213-222
  • URL: http://www.degruyter.com/view/product/184575
  • Peer Reviewed
• [Journal Article] Ordering and excitation in orbital compass model on a checkerboard lattice (2012)
  • Author(s): Joji Nasu
  • Journal Title: Phys. Rev. B Volume: 85 Issue: 20 Pages: 205141-205141
  • DOI: 10.1103/physrevb.85.205141
  • Peer Reviewed
• [Journal Article] Critical temperature and correlation length of an elastic interaction model for spin-crossover materials (2012)
  • Author(s): Taro Nakada, Takashi Mori, Seiji Miyashita, Masamichi Nishino, Synge Todo, William Nicolazzi, Per Arne Rikvold
  • Journal Title: Physical Review B Volume: 85 Issue: 5 Pages: 54408-54408
  • DOI: 10.1103/physrevb.85.054408
  • Peer Reviewed
• [Journal Article] 量子モンテカルロ法による新しい量子相・量子臨界現象の探求 (2012)
  • Author(s): 藤堂眞治
  • Journal Title: 計算工学 Volume: 17 Pages: 2841-2844
  • NAID: 10031128008
• [Journal Article] レイテンシコアの高度化・高効率化による将来のHPCIシステムに関する調査研究のためのアプリケーションと性能評価 (2012)
  • Author(s): 片桐孝洋, 大島聡史, 中島研吾, 米村崇, 熊洞宏樹, 樋口清隆, 橋本昌人, 高山恒一, 藤堂眞治, 岩田潤一, 内田和之, 佐藤正樹, 羽角博康, 黒木聖夫
  • Journal Title: 情報処理学会研究報告 (HPC) Volume: 2012-HPC-137 Pages: 1-12
  • NAID: 110009490650
• [Journal Article] Geometric allocation approach for transition kernel of Markov chain (2012)
  • Author(s): Hidemaro Suwa, Synge Todo
  • Journal Title: Monte Carlo Methods and Applications (proceedings of Eighth IMACS Seminar on Monte Carlo Methods) Volume: なし Pages: 213-222
  • Peer Reviewed
• [Journal Article] Geometric Allocation Approach for Transition Kernel of Markov Chain (2012)
  • Author(s): H. Suwa and S. Todo
  • Journal Title: IMACS Volume: 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, 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. Schollwoeck, C. Silva, B. Surer, S. Todo, S. Trebst, M. Troyer, M.L. Wall, P. Werner, S. Wessel
  • Journal Title: J. Stat. Mech Volume: P05001 Issue: 05 Pages: P05001-P05001
  • DOI: 10.1088/1742-5468/2011/05/p05001
  • 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, 藤堂眞治
  • Journal Title: 日本物理学会誌 Volume: 66 Pages: 370-370
• [Presentation] マルコフ連鎖と量子モンテカルロ, 統計力学の最近の展開 (2014)
  • Author(s): 藤堂眞治
  • Place of Presentation: 東大
  • Year and Date: 2014-03-03
• [Presentation] マルコフ連鎖と量子モンテカルロ (2014)
  • Author(s): 藤堂眞治
  • Organizer: 統計力学の最近の展開
  • Place of Presentation: 東京大学 (東京)
  • Invited
• [Presentation] Quantum Phase Transition and Universality of Quantum Spin Models with Strong Spatial Anisotropy (2013)
  • Author(s): Synge Todo
  • Organizer: Tappei Tensor Network Workshop 2013
  • Place of Presentation: Taipei
  • Year and Date: 2013-12-04
• [Presentation] Geometric Allocation Approaches in Markov Chain Monte Carlo (2013)
  • Author(s): Synge Todo
  • Organizer: ICSG2013 International Meeting on Inference, Computation, and Spin Glasses
  • Place of Presentation: Sapporo
  • Year and Date: 2013-07-28
• [Presentation] Hidemaro Suwa, Markov Chain Monte Carlo Sampling with Irreversible Kernel (2013)
  • Author(s): Synge Todo
  • Organizer: STATPHYS25 XXV IUPAP International Conference on Statistical Physics
  • Place of Presentation: Seoul
  • Year and Date: 2013-07-26
• [Presentation] Large-scale Monte Carlo Study for Exotic Phase Transitions of Strongly Correlated Quantum Magnets (2013)
  • Author(s): Synge Todo
  • Organizer: Collaborative Conference on Materials Research 2013
  • Place of Presentation: Jeju
  • Year and Date: 2013-07-26
• [Presentation] 次世代の計算物質科学に向けて (2013)
  • Author(s): 藤堂眞治
  • Organizer: 日本化学会第93春季年会
  • Place of Presentation: 立命館大
  • Year and Date: 2013-03-25
• [Presentation] 大規模並列量子モンテカルロ法ALPS/looper と量子磁性体への応用 (2013)
  • Author(s): 藤堂眞治
  • Organizer: スーパーコンピュータワークショップ2013
  • Place of Presentation: 分子研
  • Year and Date: 2013-01-23
• [Presentation] Large-scale Monte Carlo Study for Exotic Phase Transitions of Strongly Correlated Quantum Magnets (2013)
  • Author(s): Synge Todo
  • Organizer: Collaborative Conference on Materials Research 2013
  • Place of Presentation: Jeju (Korea)
  • Invited
• [Presentation] ALPS/diagonalization: Generic and Parallelized Exact Diagonalization for Quantum Lattice Models (2013)
  • Author(s): Ryo Igarashi, Tatsuya Sakashita, Synge Todo
  • Organizer: The 12th Asia Pacific Physics Conference (APPC12)
  • Place of Presentation: Makuhari Messe (Chiba)
• [Presentation] Path-Integral Monte Carlo for the Local Z2 Berry phase (2013)
  • Author(s): Yuichi Motoyama, Synge Todo
  • Organizer: The 12th Asia Pacific Physics Conference (APPC12)
  • Place of Presentation: Makuhari Messe (Chiba)
• [Presentation] Numerical Analysis of Quantum Phase Transitions with Dynamic Control of Anisotropy (2013)
  • Author(s): Shinya Yasuda, Synge Todo
  • Organizer: The 12th Asia Pacific Physics Conference (APPC12)
  • Place of Presentation: Makuhari Messe (Chiba)
• [Presentation] Markov Chain Monte Carlo Sampling with Irreversible Kernel (2013)
  • Author(s): Synge Todo, Hidemaro Suwa
  • Organizer: STATPHYS25 XXV IUPAP International Conference on Statistical Physics
  • Place of Presentation: Seoul University (Korea)
• [Presentation] Geometric Allocation Approaches in Markov Chain Monte Carlo (2013)
  • Author(s): Synge Todo
  • Organizer: ICSG2013 International Meeting on Inference, Computation, and Spin Glasses
  • Place of Presentation: Hokkaido University (Hokkaido)
  • Invited
• [Presentation] Loop Cluster Monte Carlo Simulation of Quantum Magnets Based on Global Union-find Graph Algorithm (2013)
  • Author(s): Synge Todo, Haruhiko Matsuo, Hideyuki Shitara
  • Organizer: SC13
  • Place of Presentation: Denver (USA)
• [Presentation] Quantum Phase Transition and Universality of Quantum Spin Models with Strong Spatial Anisotropy (2013)
  • Author(s): Synge Todo
  • Organizer: Tappei Tensor Network Workshop 2013
  • Place of Presentation: Taipei (Taiwan)
  • Invited
• [Presentation] 大規模並列量子モンテカルロ法ALPS/looperと量子磁性体への応用 (2013)
  • Author(s): 藤堂眞治
  • Organizer: スーパーコンピュータワークショップ2013
  • Place of Presentation: 分子研
  • Invited
• [Presentation] Next-generation quantum Monte Carlo simulation of strongly correlated materials on peta-scale supercomputer (2012)
  • Author(s): Synge Todo
  • Organizer: IEEE CPMT Symposium Japan 2012
  • Place of Presentation: Kyoto
  • Year and Date: 2012-12-12
• [Presentation] Quantum Monte Carlo level spectroscopy (2012)
  • Author(s): Synge Todo
  • Organizer: CQDC'12 International Workshop on Cooperative Quantum Dynamics and Its Control
  • Place of Presentation: Julich
  • Year and Date: 2012-10-30
• [Presentation] The ALPS project : Open source software for strongly correlated systems (2012)
  • Author(s): Synge Todo
  • Organizer: CCP2012 : Conference on Computational Physics
  • Place of Presentation: Kobe
  • Year and Date: 2012-10-17
• [Presentation] Quantum Monte Carlo level spectroscopy (2012)
  • Author(s): Synge Todo
  • Organizer: Swiss-Japan Workshop 2012 Current Topics in Theory of Correlated Materials
  • Place of Presentation: Wako
  • Year and Date: 2012-09-12
• [Presentation] 物性物理におけるモンテカルロ法とその大規模化 (2012)
  • Author(s): 藤堂眞治
  • Organizer: PC クラスタワークショップ in 柏
  • Place of Presentation: 東大柏
  • Year and Date: 2012-07-06
• [Presentation] 量子モンテカルロ法による新しい量子相・量子臨界現象の探求 (2012)
  • Author(s): 藤堂眞治
  • Organizer: 京コンピュータ・シンポジウム2012および第2回戦略プログラム5分野合同WS
  • Place of Presentation: 神戸
  • Year and Date: 2012-06-15
• [Presentation] 大規模並列量子モンテカルロ法ALPS/looper と量子磁性体への応用 (2012)
  • 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 シンポジウム
  • Place of Presentation: 神戸
  • Year and Date: 2012-03-06
• [Presentation] 物性物理におけるモンテカルロ法とその大規模化 (2012)
  • Author(s): 藤堂眞治
  • Organizer: PCクラスタワークショップ in 柏
  • Place of Presentation: 柏
  • Invited
• [Presentation] The ALPS project: Open source software for strongly correlated systems (2012)
  • Author(s): Synge Todo
  • Organizer: CCP2012: Conference on Computational Physics
  • Place of Presentation: Kobe
  • Invited
• [Presentation] 詳細つりあいを満たさないマルコフ連鎖モンテカルロ法とその応用 (2012)
  • Author(s): 藤堂眞治
  • 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RIMS
• [Presentation] ループアルゴリズム量子モンテカルロ法の MPI/OpenMP による超並列化 (2012)
  • Author(s): 松尾春彦
  • Organizer: HPCS2012 ハイパフォーマンスコンピューティングと計算科学シンポジウム(招待講演)
  • Place of Presentation: 名古屋大
• [Presentation] General Construction of Irreversible Kernel in Markov Chain Monte Carlo (2012)
  • Author(s): H. Suwa, S. Todo
  • Organizer: 10th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing
  • Place of Presentation: UNSW, Sydney, Australia
• [Presentation] 大規模並列量子モンテカルロ法ALPS/looperと量子磁性体への応用 (2012)
  • 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 シンポジウム(招待講演)
  • Place of Presentation: 神戸
• [Presentation] Topological order parameter in low-dimensional magnets - QMC measurement of local quantized Berry phase - (2011)
  • Author(s): Synge Todo, Yuichi Motoyama
  • Organizer: International Workshop on Simulation and Manipulation of Quantum Systems for Information Processing
  • Place of Presentation: Julich
  • Year and Date: 2011-10-18
• [Presentation] モンテカルロ法の発展と量子磁性体への応用 (2011)
  • Author(s): 藤堂眞治
  • Organizer: 計算物質科学研究センター第1回シンポジウム
  • Place of Presentation: 物性研
  • Year and Date: 2011-09-13
• [Presentation] Nonreversible Quantum Monte Carlo Analysis for Spin-Peierls Transition (2011)
  • Author(s): H. Suwa and S. Todo
  • Organizer: International Workshop on Recent Developments of Studies on Phase Transitions
  • Place of Presentation: Tokyo
• [Presentation] Geometric Allocation Approach for Transition Kernel of Markov Chain (2011)
  • Author(s): H. Suwa, S. Todo
  • Organizer: Eighth IMACS Seminar on Monte Carlo Methods
  • Place of Presentation: Borovetz, Bulgaria
• [Presentation] Topological order parameter in low-dimensional magnets - QMC measurement of local quantized Berry phase - (2011)
  • Author(s): Synge Todo and Yuichi Motoyama
  • Organizer: International Workshop on Simulation and Manipulation of Quantum Systems for Information Processing(招待講演)
  • Place of Presentation: Julich, Germany
• [Book] Loop Algorithm, in Strongly Correlated Systems : Numerical Methods (Springer Series in Solid-State Sciences), ed. A. Avella, F. Mancini (2013)
  • Author(s): Synge Todo
  • Publisher: Springer-Verlag, Berlin
• [Book] Loop Algorithm, in Strongly Correlated Systems: Numerical Methods (Springer Series in Solid-State Sciences) (2013)
  • Author(s): Synge Todo
  • Total Pages: 325
  • Publisher: Springer-Verlag
• [Remarks]
  • URL: http://exa.phys.s.u-tokyo.ac.jp/ja
• [Remarks]
  • URL: http://alps.comp-phys.org
• [Remarks]
  • URL: https://github.com/cmsi/bcl
• [Remarks]
  • URL: https://github.com/wistaria/worms
• [Remarks] BCL: Balance Condition Library
  • URL: https://github.com/cmsi/bcl
• [Remarks] Worms: a simple worm code
  • URL: https://github.com/wistaria/worms
• [Remarks] Rokko: Integrated interface for eigenvalue problem
  • URL: https://github.com/t-sakashita/rokko
• [Remarks] 藤堂研究室
  • URL: http://exa.phys.s.u-tokyo.ac.jp