Study of quantum correlation and topological order in low-dimensional quantum spin systems

• Project/Area Number: 26400384
• 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, 大学院理学系研究科(理学部), 准教授 (10291337)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 計算物理 / 量子モンテカルロ / トポロジカル秩序 / 量子スピン系 / 量子相転移 / 動的臨界現象 / 長距離相互作用 / ボーズ・ハバード模型 / トポロジカルオーダー / テンソルネットワーク

Outline of Final Research Achievements

We have extended "topological order parameter," which characterizes various quantum states and novel quantum phase transitions in low-dimensional quantum spin systems, to high dimensions, and developed methods for measuring these order parameters with high accuracy. We have also combined the Monte Carlo method with machine learning technique, which enables precise analysis of dynamical critical phenomena. We have performed large-scale quantum Monte Carlo simulations and analyzed various quantum phase transitions and quantum states.

Research Products

• [Journal Article] Upper and lower critical decay exponents of Ising ferromagnet with long-range interaction (2017)
  • Author(s): Toshiki Horita, Hidemaro Suwa, Synge Todo
  • Journal Title: Phys. Rev. E Volume: 95 Issue: 1 Pages: 012143-012143
  • DOI: 10.1103/physreve.95.012143
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Updated Core Libraries of the ALPS Project (2017)
  • Author(s): A. Gaenko, A. E. Antipov, G. Carcassi, T. Chen, X. Chen, Q. Dong, L. Gamper, J. Gukelberger, R. Igarashi, S. Iskakov, M. Konz, J. P. F. LeBlanc, R. Levy, P. N. Ma, J. E. Paki, H. Shinaoka, S. Todo, M. Troyer, E. Gull
  • Journal Title: Computer Physics Communications Volume: 213 Pages: 235-251
  • DOI: 10.1016/j.cpc.2016.12.009
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Quantum Lattice Model Solver HΦ (2017)
  • Author(s): Mitsuaki Kawamura, Kazuyoshi Yoshimi, Takahiro Misawa, Youhei Yamaji, Synge Todo, Naoki Kawashima
  • Journal Title: Comp. Phys. Comm. Volume: 印刷中
  • Peer Reviewed / Open Access
• [Journal Article] 特集「『京』が拓いた物性物理」について (2016)
  • Author(s): 渡辺宙志, 藤堂眞治
  • Journal Title: 分子シミュレーション研究会会誌 アンサンブル Volume: 18 Pages: 5-6
  • NAID: 130005312260
• [Journal Article] Generalized Moment Method for Gap Estimation and Quantum Monte Carlo Level Spectroscopy (2015)
  • Author(s): Hidemaro Suwa, Synge Todo
  • Journal Title: Phys. Rev. Lett. Volume: 115 Issue: 8
  • DOI: 10.1103/physrevlett.115.080601
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Stochastic approximation of dynamical exponent at quantum critical point (2015)
  • Author(s): Shinya Yasuda, Hidemaro Suwa, Synge Todo
  • Journal Title: Phys. Rev. B Volume: 92 Issue: 10
  • DOI: 10.1103/physrevb.92.104411
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] "実験技術"としての量子多体系シミュレーションソフトウェア ALPS (2015)
  • Author(s): 藤堂眞治
  • Journal Title: 日本物理学会誌 Volume: 70 Pages: 275-282
  • Peer Reviewed
• [Journal Article] MateriApps --- a Portal Site of Materials Science Simulation (2015)
  • Author(s): Yusuke Konishi, Ryo Igarashi, Shunsuke Kasamatsu, Takeo Kato, Naoki Kawashima, Tsutomu Kawatsu, Hikaru Kouta, Masashi Noda, Shoichi Sasaki, Yayoi Terada, Synge Todo, Shigehiro Tsuchida, Kazuyoshi Yoshimi, Kanako Yoshizawa
  • Journal Title: JPS Conf. Proc. Volume: 5 Pages: 011007-011007
  • DOI: 10.7566/jpscp.5.011007
  • Peer Reviewed
• [Journal Article] Thermal phase transition of generalized Heisenberg models for SU(N) spins on square and honeycomb lattices (2015)
  • Author(s): Takafumi Suzuki, Kenji Harada, Haruhiko Matsuo, Synge Todo and Naoki Kawashima
  • Journal Title: Phys. Rev. B Volume: 91 Issue: 9 Pages: 094414-094414
  • DOI: 10.1103/physrevb.91.094414
  • NAID: 120005619792
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [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
• [Presentation] Dynamical property of strongly anisotropic quantum criticality in random spin systems (2017)
  • Author(s): Synge Todo
  • Organizer: Workshop on quantum dynamics and response
  • Place of Presentation: 東大 (文京区・東京)
  • Int'l Joint Research
• [Presentation] Stochastic Approximation of Dynamical Exponent at Quantum Critical Point (2016)
  • Author(s): Hidemaro Suwa, Shinya Yasuda, Synge Todo
  • Organizer: APS March Meeting 2016
  • Place of Presentation: Baltimore (USA)
  • Year and Date: 2016-03-16
  • Int'l Joint Research
• [Presentation] MateriApps: a Portal to Materials Science Simulation (2016)
  • Author(s): Synge Todo
  • Organizer: Supercomputing Frontiers Singapore 2016
  • Place of Presentation: Singapore (Singapore)
  • Year and Date: 2016-03-15
  • Int'l Joint Research
• [Presentation] Quantum criticality with strong space-time anisotropy (2016)
  • Author(s): Synge Todo
  • Organizer: LMU-UT Workshop
  • Place of Presentation: 東京大学 (東京都文京区)
  • Year and Date: 2016-02-29
  • Int'l Joint Research
• [Presentation] 確率的最適化によるランダムスピン系の量子臨界現象の研究 (2016)
  • Author(s): 藤堂眞治
  • Organizer: 物性研究所スパコン共同利用・CCMS合同研究会「計算物質科学の今と未来」
  • Place of Presentation: 東大物性研 (千葉県・柏市)
  • Invited
• [Presentation] Critical Decay Exponent of Ising Ferromagnet with Long-range Interaction (2016)
  • Author(s): Synge Todo
  • Organizer: 2nd Conference on Condensed Matter Physics
  • Place of Presentation: Nanjing (China)
  • Int'l Joint Research / Invited
• [Presentation] Material Science Simulation by MateriApps LIVE! (2016)
  • Author(s): 藤堂眞治, 加藤岳生
  • Organizer: TIAポスター交流会
  • Place of Presentation: エポカルつくば (茨城県・つくば市)
• [Presentation] MateriApps による物質科学シミュレーション～MateriApps LIVE! と格子模型計算 (2016)
  • Author(s): 藤堂眞治, 加藤岳生
  • Organizer: 日本物理学会2016年秋季大会
  • Place of Presentation: 金沢大 (金沢市・石川県)
• [Presentation] MateriApps: a Portal for Materials Science Simulation (2015)
  • Author(s): Synge Todo, Ryo Igarashi, Shusuke Kasamatsu, Takeo Kato, Naoki Kawashima, Tsutomu Kawatsu, Yusuke Konishi, Hikaru Kouta, Haruhiko Matsuo, Masashi Noda, Shoichi Sasaki, Yayoi Terada, Shigehiro Tsuchida, Kazuyoshi Yoshimi, Kanako Yoshizawa
  • Organizer: SC15
  • Place of Presentation: Austin (USA)
  • Year and Date: 2015-11-18
  • Int'l Joint Research
• [Presentation] ランダムネス存在下における量子相転移の動的臨界指数測定 (2015)
  • Author(s): 安田真也, 諏訪秀麿, 藤堂眞治
  • Organizer: 日本物理学会2015年秋季大会
  • Place of Presentation: 関西大学 (大阪府吹田市)
  • Year and Date: 2015-09-17
• [Presentation] Geometric Allocation Approaches in Markov Chain Monte Carlo (2014)
  • Author(s): Synge Todo
  • Organizer: Joint Workshop on Physics UT and ENS
  • Place of Presentation: パリ(フランス)
  • Year and Date: 2014-12-09
• [Presentation] 物質科学シミュレーションのポータルサイト「MateriApps」/強相関電子系・スピン系の汎用シミュレーションソフトウェア「ALPS」 (2014)
  • Author(s): 藤堂眞治
  • Organizer: 物性研究所計算物質科学研究センター 第4回シンポジウム
  • Place of Presentation: 物性研 (柏, 千葉 )
  • Year and Date: 2014-11-12
  • Invited
• [Presentation] K-computer study of quantum phase transitions in two-dimensional magnets (2014)
  • Author(s): Synge Todo
  • Organizer: Cooperation in Physics Workshop: UT-LMU
  • Place of Presentation: ミュンヘン(ドイツ)
  • Year and Date: 2014-10-28
• [Presentation] 物質科学シミュレーションのポータルサイト「MateriApps」/強相関電子系・スピン系の汎用シミュレーションソフトウェア「ALPS」 (2014)
  • Author(s): 藤堂眞治
  • Organizer: 第１回「京」と大型実験施設との連携利用シンポジウム
  • Place of Presentation: 秋葉原Next-1 (東京)
  • Year and Date: 2014-09-02
  • Invited
• [Remarks] 藤堂研究室
  • URL: http://exa.phys.s.u-tokyo.ac.jp
• [Remarks] worms: a simple worm code
  • URL: https://github.com/wistaria/worms
• [Remarks] ALPSCore
  • URL: http://alpscore.org
• [Remarks] HΦ: 並列計算機に対応した数値厳密対角化法による有効模型ソルバーパッケージ
  • URL: http://ma.cms-initiative.jp/ja/listapps/hphi
• [Remarks] Kω: シフト型クリロフ部分空間法に基づく線形演算ライブラリ
  • URL: http://ma.cms-initiative.jp/ja/listapps/komega