The exact WKB analysis on correlation functions of low dimensional quantum systems and quantum entanglement.

• Project/Area Number: 20540370
• 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: Shizuoka University
• Principal Investigator: SUZUKI Junji Shizuoka University, 理学部, 教授 (40222062)
• Co-Investigator(Renkei-kenkyūsha): KUNIBA Atsuo 東京大学, 大学院・総合文化研究科, 教授 (70211886) ; NAKANISHI Tomoki 名古屋大学, 大学院・多元数理研究科, 准教授 (80227842)
• Research Collaborator: ANDREAS Kluemper ブッパタール大学, 教授 ; FRANK Goehmann ブッパタール大学, 講師
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 可積分系 / 厳密WKB法 / 量子スピン / 相関関数 / 量子もつれ / 関数等式 / 完全WKB法 / クラスター代数 / concurrence / 量子・古典クロスオーバー / 密度行列

Research Abstract

We develop a novel formulation in an exact quantitative study on the correlation functions of 1D quantum systems at finite temperature. This is accomplished by combining the quantum transfer method and the exact WKB method.
The formulation enables us to carry a rigorous numerical study on the quantum correlations. As a concrete example, we apply it to the spin 1/2 quantum XXZ chain.
The variety of behaviors of the correlation functions and quantum entanglement is observed as we change the system temperature and an applied magnetic field.

Research Products

• [Journal Article] T-systems and Y-systems in integrable systems (2011)
  • Author(s): A.Kuniba,T.Nakanishi, J.Suzuki
  • Journal Title: J.Phys.A : Math.Theor. Vol 44 Pages: 146-146
  • Peer Reviewed
• [Journal Article] T-systems and Y-systems in integrable systems (2011)
  • Author(s): A.Kuniba, T.Nakanishi, J.Suzuki
  • Journal Title: J.Phys.A : Math.Theor.. Volume: 44(電子ジャーナル) Pages: 146-146
  • Peer Reviewed
• [Journal Article] Correlation functions of the integrable isotropic spin-1 chain at finite temperature (2010)
  • Author(s): F.Goehmann, A.Seel, J.Suzuki
  • Journal Title: Journal of Statistical Mechanics 11011 Pages: 42-42
  • Peer Reviewed
• [Journal Article] Periodicities of T-systems and Y-systems (2010)
  • Author(s): R.Inoue, O.Iyama, A.Kuniba, T.Nakanishi, J.Suzuki
  • Journal Title: Nagoya Mathematical Journal Vol 197 Pages: 59-174
  • Peer Reviewed
• [Journal Article] 可積分系の数学～ソリトンを源流として～ (2010)
  • Author(s): 鈴木淳史
  • Journal Title: 数理科学 Pages: 64-69
• [Journal Article] Symmetry (2010)
  • Author(s): A.Kuniba, T.Nakanishi, J.Suzuki
  • Journal Title: Integrability and Geometry : Method and Applications Vol 5 Pages: 23-23
  • Peer Reviewed
• [Journal Article] Correlation functions of the integrable isotropicspin-1 chain at finite temperature (2010)
  • Author(s): F.Gohmann, A.Seel, J.Suzuki
  • Journal Title: Journal of Statistical Mechanics : theory and experiment Volume: P11011(電子ジャーナル) Pages: 42-42
  • Peer Reviewed
• [Journal Article] Periodicities of T- systems and Y- systems (2010)
  • Author(s): R.Inoue, O.Iyama, A.Kuniba, T.Nakanishi, J.Suzuki
  • Journal Title: Nagoya Mathematical Journal 197 Pages: 59-174
  • Peer Reviewed
• [Journal Article] T- systems and Y- systems for quantum affinizations of quantum Kac- Moody algebras (2010)
  • Author(s): A.Kuniba, T.Nakanishi, J.Suzuki
  • Journal Title: Symmetry, Integrability and Geometry : Method and Applications 5 Pages: 108-108
  • Peer Reviewed
• [Journal Article] 可積分系と統計力学 (2009)
  • Author(s): 鈴木淳史
  • Journal Title: 数理科学 Pages: 28-33
• [Journal Article] Short-distance thermal correlations in the XXZ chain (2008)
  • Author(s): H. Boos, J.Damerau, F.Gohmaim, A.Klumper, J.Suzuki, A.Weisse
  • Journal Title: Journal of Statistical Mechanics 0808 Pages: 25-25
  • Peer Reviewed
• [Journal Article] Short-distance thermal correlations in the XXZ chain (2008)
  • Author(s): H. Boos, J. Damerau, F Gohmann, A. Klumper, J. Suzuki, A. Weisse
  • Journal Title: Journal of Statistical Mechanics 0808(電子ジャーナル)
  • Peer Reviewed
• [Presentation] ODE/IM対応 (2010)
  • Author(s): 鈴木淳史
  • Organizer: 可積分系数理の多様性
  • Place of Presentation: 京都大学数理解析研究所、京都市
  • Year and Date: 2010-08-18
• [Presentation] ODE/IM対応 (2010)
  • Author(s): 鈴木淳史
  • Organizer: 可積分系数理の多様性
  • Place of Presentation: 京都大学数理解析研究所(京都市).
  • Year and Date: 2010-08-18
• [Presentation] The dark side of higher spin chains (2010)
  • Author(s): 鈴木淳史
  • Organizer: Exactly solvable models in statistical mechanics
  • Place of Presentation: University of Queensland(Brisbane, Australia))
  • Year and Date: 2010-07-14
• [Presentation] The dark side of higher spin chains (2010)
  • Author(s): J.Suzuki
  • Organizer: Exactly solvable models in statistical mechanics
  • Place of Presentation: University of Queensland(Brisbane, Australial)
  • Year and Date: 2010-07-14
• [Presentation] Quantum-Classical Crossover Revisited (2010)
  • Author(s): 鈴木淳史
  • Organizer: Condensed Matter Physics Meets High Energy Physics
  • Place of Presentation: 東京大学(IPMU)柏市)
  • Year and Date: 2010-02-11
• [Presentation] Quantum-Classical Crossover Revisited (2010)
  • Author(s): 鈴木淳史
  • Organizer: Condensed Matter Physics Meets High Energy Physics
  • Place of Presentation: 東京大学 (IPMU)
  • Year and Date: 2010-02-11
• [Presentation] One dimensional quantum spin chain at finite temperatures (2009)
  • Author(s): 鈴木淳史
  • Organizer: Infinite analysis 09
  • Place of Presentation: 京都大学理学部、京都市
  • Year and Date: 2009-07-27
• [Presentation] One dimensional quantum spin chain at finite tempreatures (2009)
  • Author(s): 鈴木淳史
  • Organizer: Infinite analysis 09
  • Place of Presentation: 京都大学理学部
  • Year and Date: 2009-07-27
• [Presentation] T-systemの周期性について (2009)
  • Author(s): 井上玲
  • Organizer: 日本数学会
  • Place of Presentation: 東京大学、目黒区
  • Year and Date: 2009-03-29
• [Presentation] T-systemの周期既について (2009)
  • Author(s): 井上玲
  • Organizer: 日本数学会年会
  • Place of Presentation: 東京大学駒場キャンパス
  • Year and Date: 2009-03-29
• [Presentation] Finite temperature matrix elements (2008)
  • Author(s): 鈴木淳史
  • Organizer: Low Dimensional Quantum Field Theories and Applications
  • Place of Presentation: ガリレオガリレイ研究所(フィレンチェ・イタリア)
  • Year and Date: 2008-10-02
• [Presentation] Finite temperature density matrix elements (2008)
  • Author(s): 鈴木淳史
  • Organizer: Low Dimensional Quantum Field Theories and Applications
  • Place of Presentation: ガリレオガリレイ研究所(フィレンチエ)
  • Year and Date: 2008-10-02
• [Presentation] Finite temperature correlation functions (2008)
  • Author(s): 鈴木淳史
  • Organizer: Finite Size technology in low dimensional quantum field system IV
  • Place of Presentation: APCTP(浦項・韓国)
  • Year and Date: 2008-07-02
• [Book] Quantum spin chains at finite temperatures("New trands in Quantum integrable systems") (2010)
  • Author(s): F.Goehmann, J.Suzuki
  • Total Pages: 20
  • Publisher: World Scientific
• [Book] Quantum spin chains at finite temperatures ("New trands in Quantum integrable systems") (2010)
  • Author(s): F.Gohmann, J.Suzuki
  • Publisher: World Scientific
• [Book] New Trends in Mathematical Physics (2009)
  • Author(s): P.Dorey, C.Dunning, D.Masoero, J.Suzuki, R.Tateo
  • Total Pages: 11
  • Publisher: Springer
• [Book] 可積分模型の項(広中平祐編集)(数理科学辞典)(物理の数学) (2009)
  • Author(s): 鈴木淳史
  • Total Pages: 7
  • Publisher: 丸善出版
• [Book] 数理科学辞典 (広中平祐編集) 物理の数学「可積分模型」の項 (2009)
  • Author(s): 鈴木淳史
  • Total Pages: 7
  • Publisher: 丸善
• [Book] New Trends in Mathematical Physics (2009)
  • Author(s): P.Dorey, C.Dunning, D.Masoero, 鈴木淳史, R.Tateo
  • Total Pages: 11
  • Publisher: Springer
• [Remarks] ホームページ等
  • URL: http://www.ipc.shizuoka.ac.jp/~sjsuzuk/js-shizuoka-japanese.html