Geometric Approach to Markov Chain Monte Carlo

2013 Fiscal Year Final Research Report

• 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
• 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

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: 012130
  • 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: 012127
  • 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 Pages: 140603
  • DOI: 10.1103/PhysRevLett.112.140603
  • Peer Reviewed
• [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: 012013
  • 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 Volume: E88 Pages: 061301(R)
  • 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 Pages: 220408(R)
  • 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 the Spatially Anisotropic Triangular Lattice (2013)
  • Author(s): H. Nakano, S. Todo, T. Sakai
  • Journal Title: J. Phys. Soc. Jpn Volume: 82 Pages: 043715
  • DOI: 10.7566/JPSJ.82.043715
  • 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 Pages: 021301(R)
  • 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): J. Nasu, S. Todo, S. Ishihara
  • Journal Title: Phys. Rev Volume: B85 Pages: 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): T. Nakada, T. Mori, S. Miyashita, M. Nishino, S. Todo, W. Nicolazzi, P. A. Rikvold
  • Journal Title: Phys. Rev Volume: B85 Pages: 054408
  • DOI: 10.1103/PhysRevB.85.054408
  • 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
  • DOI: 10.1088/1742-5468/2011/05/P05001
  • Peer Reviewed
• [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] 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] 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] 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
• [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
  • Total Pages: 153-184
  • Publisher: Springer-Verlag, Berlin
• [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