Classification of quantum critical phenomena based on entanglement

• Project/Area Number: 25400392
• 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: OSHIKAWA Masaki 東京大学, 物性研究所, 教授 (50262043)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
• Keywords: 量子多体系におけるエンタングルメント / 量子反強磁性体 / エンタングルメント・スペクトル / 朝永・ラッティンジャー流体 / 場の理論 / 量子異常 / 相の分類 / 対称性による保護 / エンタングルメント / トポロジカル相 / 量子スピン系 / 量子ホール状態 / 国際研究者交流 / 量子エンタングルメント / 朝永・ラッティンジャー液体 / バレンス・ボンド / 国際情報交換 アメリカ合衆国 / 国際研究者交流 フランス

Outline of Final Research Achievements

Stimulated by the recent substantial progress in the classification of gapped topological phases, we proposed and formulated several novel concepts for classification of gapless quantum critical phases, which is a major open problem. For example, we found that the valence-bond distribution in the ground state of a quantum antiferromagnet follows a universal scaling which reflects the nature of the ground state. Moreover, we obtained the entanglement spectrum between two coupled Tomonaga-Luttinger liquids. In particular, when the gap is partially opened by the interchain interaction, the entanglement spectrum exhibits a peculiar dispersion relation in which the entanglement energy is proportional to the square root of the momentum along the chain. In both cases, analytical prediction was confirmed by numerical calculations.

Research Products

• [Int'l Joint Research] CEA(フランス)
• [Int'l Joint Research] Max-Planck Institute PKS(ドイツ)
• [Int'l Joint Research] University of Geneva(スイス)
• [Journal Article] Distinct trivial phases protected by a point-group symmetry in quantum spin chain (2015)
  • Author(s): Yohei Fuji, Frank Pollmann, Masaki Oshikawa
  • Journal Title: Physical Review Letters Volume: 印刷中
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Quantum criticality in an asymmetric three-leg spin tube: A strong rung-coupling perspective (2014)
  • Author(s): Yohei Fuji, Satoshi Nishimoto, Hitoshi Nakada, and Masaki Oshikawa
  • Journal Title: Phys. Rev. B Volume: 89 Issue: 5
  • DOI: 10.1103/physrevb.89.054425
  • Peer Reviewed
• [Journal Article] Valence bond distribution and correlation in bipartite Heisenberg antiferromagnets (2014)
  • Author(s): David Schwandt, Fabien Alet, and Masaki Oshikawa
  • Journal Title: Phys. Rev. B Volume: 89 Issue: 10
  • DOI: 10.1103/physrevb.89.104416
  • Peer Reviewed
• [Journal Article] Entanglement spectra between coupled Tomonaga-Luttinger liquids: Applications to ladder systems and topological phases (2013)
  • Author(s): Rex Lundgren, Yohei Fuji, Shunsuke Furukawa, and Masaki Oshikawa
  • Journal Title: Phys. Rev. B Volume: 88 Issue: 24
  • DOI: 10.1103/physrevb.88.245137
  • Peer Reviewed
• [Presentation] Symmetry protection of critical phases and global anomaly in 1+1 dimensions (2016)
  • Author(s): Masaki Oshikawa
  • Organizer: Topological Science Kick-off Symposium 2016
  • Place of Presentation: 慶応大学日吉キャンパス (神奈川県・横浜市）
  • Year and Date: 2016-03-14
  • Int'l Joint Research / Invited
• [Presentation] Flux Quench in Interacting Spinless Fermions in One Dimension (2016)
  • Author(s): Masaki Oshikawa
  • Organizer: Mathematical Aspects of Quantum Integrable Models in and out of Equilibrium
  • Place of Presentation: Isaac Newton Institute for Mathematical Sciences, University of Cambridge (UK)
  • Year and Date: 2016-02-04
  • Int'l Joint Research / Invited
• [Presentation] Entanglement and Shannon-Renyi Entropies in Quantum Many-Body Systems (2016)
  • Author(s): Masaki Oshikawa
  • Organizer: YITP Workshop in Quantum Information Physics 2016
  • Place of Presentation: 京都大学基礎物理学研究所 (京都府・京都市）
  • Year and Date: 2016-01-05
  • Int'l Joint Research / Invited
• [Presentation] Symmetry-Protected trivial Phases in One Dimension (2015)
  • Author(s): Masaki Oshikawa
  • Organizer: Entanglement at Fudan
  • Place of Presentation: Fudan University, Shanghai (China)
  • Year and Date: 2015-12-17
  • Int'l Joint Research / Invited
• [Presentation] Entanglement and Shannon-Renyi Entropies in Quantum Many-Body Systems (2015)
  • Author(s): Masaki Oshikawa
  • Organizer: Entanglement at Fudan
  • Place of Presentation: Fudan University, Shanghai (China)
  • Year and Date: 2015-12-17
  • Int'l Joint Research / Invited
• [Presentation] Symmetry Protection of Critical Phases and Global Anomaly in 1+1 Dimensions (2015)
  • Author(s): Masaki Oshikawa
  • Organizer: KEK Theory Workshop 2015 Dec.
  • Place of Presentation: 高エネルギー加速器研究機構 (茨城県・つくば市）
  • Year and Date: 2015-12-01
  • Int'l Joint Research / Invited
• [Presentation] Symmetry protection of critical phases and global anomaly in 1+1 dimensions (2015)
  • Author(s): Masaki Oshikawa
  • Organizer: Strongly Interacting Topological Phases
  • Place of Presentation: Banff International Research Station, Banff, AB (Canada)
  • Year and Date: 2015-09-20
  • Int'l Joint Research / Invited
• [Presentation] 一次元スピンレスフェルミオン系における磁束クエンチ (2015)
  • Author(s): 中川裕也, Gregoire Misguich, 押川正毅
  • Organizer: 日本物理学会2015年秋季大会
  • Place of Presentation: 関西大学千里山キャンパス (大阪府・吹田市）
  • Year and Date: 2015-09-16
• [Presentation] 2次元量子反強磁性相におけるShannon-Renyiエントロピー (2015)
  • Author(s): Gregoire Misguich, Vincent Pasquier, 押川正毅
  • Organizer: 日本物理学会2015年秋季大会
  • Place of Presentation: 関西大学千里山キャンパス (大阪府・吹田市）
  • Year and Date: 2015-09-16
• [Presentation] Symmetry Protection of Critical Phases (2015)
  • Author(s): Masaki Oshikawa
  • Organizer: Beyond Quasiparticles: New Paradigms for Quantum Fluids, Aspen Center for Physics
  • Place of Presentation: Aspen Center for Physics, Aspen, CO (USA)
  • Year and Date: 2015-08-17
  • Int'l Joint Research / Invited
• [Presentation] Symmetry protection of critical phases and global anomaly in 1+1 dimensions (2015)
  • Author(s): Masaki Oshikawa
  • Organizer: Holographic duality for condensed matter physics
  • Place of Presentation: Kavli Institute for Theoretical Physics China, Beijing (China)
  • Year and Date: 2015-07-06
  • Int'l Joint Research / Invited
• [Presentation] Entanglement/Valence Bond/Shannon Entropies and Boundary Field Theory (2015)
  • Author(s): Masaki Oshikawa
  • Organizer: Entanglement in Strongly-Correlated Quantum Matter
  • Place of Presentation: Kavli Institute for Theoretical Physics, UC Santa Barbara, CA (USA)
  • Year and Date: 2015-05-18
  • Int'l Joint Research / Invited
• [Presentation] Symmetry protection of critical phases and global anomaly in 1+1 dimensions (2015)
  • Author(s): Masaki Oshikawa
  • Organizer: Dynamics of Strongly Correlated Systems
  • Place of Presentation: 東京大学物性研究所（千葉県柏市）
  • Year and Date: 2015-03-30 – 2015-03-31
  • Invited
• [Presentation] 空間反転対称性によって守られた1次元ボゾン系のギャップ相 (2015)
  • Author(s): 藤陽平、Frank Pollmann、押川正毅
  • Organizer: 日本物理学会第７０回年会
  • Place of Presentation: 早稲田大学早稲田キャンパス（東京都新宿区）
  • Year and Date: 2015-03-21 – 2015-03-24
• [Presentation] 1次元系のSPT相と量子相転移 (2014)
  • Author(s): 押川正毅
  • Organizer: 日本物理学会2014年秋季大会【物性関係】 シンポジウム
  • Place of Presentation: 中部大学春日井キャンパス（愛知県春日井市）
  • Year and Date: 2014-09-07 – 2014-09-10
  • Invited
• [Presentation] 結合したTomonaga-Luttinger液体間のエンタングルメントスペクトラム (2014)
  • Author(s): 藤陽平、Rex Lundgren、古川俊輔、押川正毅
  • Organizer: 日本物理学会2014年秋季大会
  • Place of Presentation: 中部大学春日井キャンパス（愛知県春日井市）
  • Year and Date: 2014-09-07 – 2014-09-10
• [Presentation] Symmetry-protected trivial phases in one dimension (2014)
  • Author(s): Masaki Oshikawa
  • Organizer: Numerical and analytical methods for strongly correlated systems
  • Place of Presentation: CCBPP (Benasque, Spain)
  • Year and Date: 2014-08-24 – 2014-09-13
  • Invited
• [Presentation] Symmetry-protected trivial phases in one dimension (2014)
  • Author(s): Masaki Oshikawa
  • Organizer: Topology and Entanglement in Correlated Quantum Systems
  • Place of Presentation: MPIPKS (Dresden, Germany)
  • Year and Date: 2014-07-21 – 2014-07-25
  • Invited
• [Presentation] 二分格子上のS=1/2ハイゼンベルグ反強磁性体におけるバレンスボンドの分布と相関 (2014)
  • Author(s): David Schwandt，Fabien Alet，○押川正毅
  • Organizer: 日本物理学会 第６９回年次大会
  • Place of Presentation: 東海大学（神奈川県）
• [Presentation] 量子多体系におけるエンタングルメントと幾何学 (2014)
  • Author(s): 押川正毅
  • Organizer: 日本物理学会 第６９回年次大会
  • Place of Presentation: 東海大学（神奈川県）
  • Invited
• [Presentation] 対称性によって守られたHaldane相：場の理論によるアプローチ (2014)
  • Author(s): 藤陽平，押川正毅
  • Organizer: 日本物理学会 第６９回年次大会
  • Place of Presentation: 東海大学（神奈川県）
• [Presentation] Single-ion anisotropy in Haldane chains and form factor of the O(3) nonlinear sigma model (2013)
  • Author(s): Masaki Oshikawa
  • Organizer: IEU Workshop on Integrability & CFT
  • Place of Presentation: Institute for Early Universe, Ewha Womans University, Seoul, Korea
  • Invited
• [Presentation] J1-J3-J4モデルの量子相転移のユニバーサリティークラス (2013)
  • Author(s): 毛利 宗一朗, 古谷 峻介, 藤 陽平, 高吉 慎太郎, 押川 正毅
  • Organizer: 日本物理学会 ２０１３年秋季大会
  • Place of Presentation: 徳島大学（徳島県）
• [Presentation] 有限温度相転移における相互情報量の場の理論による解析 (2013)
  • Author(s): 熊野裕太，押川正毅
  • Organizer: 日本物理学会 ２０１３年秋季大会
  • Place of Presentation: 徳島大学（徳島県）