Theory and application of mathematical analysis on 1D Bose systems

• Project/Area Number: 24540399
• 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: Shizuoka University
• Principal Investigator: Suzuki Junji 静岡大学, 理学部, 教授 (40222062)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 量子相関 / 可積分系 / 量子転送行列法 / 厳密WKB法 / フレッドホルム行列 / ボーズ粒子 / 量子逆散乱法 / 完全WKB法 / 反強磁性ハイゼンベルグ模型 / 形状因子 / 量子転送行列 / 国際研究者交流（ドイツ・フランス） / リーマンゼータ関数 / 国際情報交換（ドイツ) / 国際情報交換 ドイツ

Outline of Final Research Achievements

We have developed an analytic framework to deal with mathematical problems arising from the quantum correlations in one dimensional Bose system and related models of finite and infinite size. It combines the method of quantum transfer matrix and the exact WKB method. We have obtained exact, concrete and quantitative results in various physical systems. In particular we have analyzed correlation functions in higher spin chains which reduces to the Bose system in a scaling limit. Then a hidden link between this physical system and the Riemann's zeta function has been found. We also analyzed the so called thermodynamic Bethe ansatz for the wider class of supersymmetric systems
which generalizes the Bose system. We have found analytic solutions to these equations for the first time. By applying this machinery, we predict theoretically the existence of three different time regimes in the dynamics of anisotropic Heisenberg spin chains.

Research Products

• [Int'l Joint Research] ブッパタール大学(ドイツ)
• [Int'l Joint Research] ブルゴーニュ大学(フランス)
• [Journal Article] Asymptotics of correlation functions of the Heisenberg-Ising chain in the easy-axis regime (2016)
  • Author(s): M. Dugave, F. Gohmann, K. K. Kozlowski, J.Suzuki
  • Journal Title: Journal of Physics A Volume: 49 Issue: 7 Pages: 1-11
  • DOI: 10.1088/1751-8113/49/7/07lt01
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] On form-factor expansions for the XXZ chain in the massive regime (2015)
  • Author(s): M. Dugave, F. Gohmann, K. K. Kozlowski, J. Suzuki
  • Journal Title: Journal of Statistical Mechanics Volume: 5 Pages: 1-47
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Elementary functions in thermodynamic Bethe ansatz (2015)
  • Author(s): J. Suzuki
  • Journal Title: Journal of Physics A Volume: 48 Issue: 20 Pages: 1-27
  • DOI: 10.1088/1751-8113/48/20/205204
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling (2014)
  • Author(s): Y. Hatsuda, K. Ito, Y. Satoh and J. Suzuki
  • Journal Title: Journal of High Energy Physics Volume: 408 Issue: 8 Pages: 162-162
  • DOI: 10.1007/jhep08(2014)162
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Correlation functions of the integrable isotropic spin-1 chain : algebraic expressions for finite temperature (2013)
  • Author(s): A. Klumper, D. Nawrath and J. Suzuki
  • Journal Title: Journal of Statistical Mechanics Volume: P08009 Issue: 08 Pages: 1-38
  • DOI: 10.1088/1742-5468/2013/08/p08009
  • Peer Reviewed
• [Presentation] Correlation functions of the Heisenberg-Ising chain (2015)
  • Author(s): Junji Suzuki
  • Organizer: Baxter 2015:Integrability and Beyond
  • Place of Presentation: ケアンズ（オーストラリア）
  • Year and Date: 2015-07-19
  • Int'l Joint Research / Invited
• [Presentation] Form factor expansion of the correlation functions of the spin 1/2 XXZ model in a massive regime (2015)
  • Author(s): Junji Suzuki
  • Organizer: "Aspects of Integrability in Mathematics and Physics"
  • Place of Presentation: 大阪市立大学理学部（大阪府）
  • Year and Date: 2015-03-09 – 2015-03-11
  • Invited
• [Presentation] Elementary functions in N=2 SUSY TBA (2014)
  • Author(s): Junji Suzuki
  • Organizer: "Integrability in gauge-gravity duality and strong coupling dynamics of gauge theory"
  • Place of Presentation: 京都大学理学部（京都府）
  • Year and Date: 2014-09-22 – 2014-09-23
  • Invited
• [Presentation] Correlations in massive phase (2014)
  • Author(s): Junji Suzuki
  • Organizer: "Recent Advances in the Theory of Quantum Integrable Systems "
  • Place of Presentation: University of Burgundy (Dijon, France)
  • Year and Date: 2014-09-01 – 2014-09-05
• [Presentation] Elementary functions in TBA (2014)
  • Author(s): Junji Suzuki
  • Organizer: "Integrable lattice models and quantum field theories"
  • Place of Presentation: Phyzik Zentrum (Bad Honnef , Germany)
  • Year and Date: 2014-06-28 – 2014-07-02
  • Invited
• [Presentation] Applied ODE/IM (2014)
  • Author(s): J. Suzuki
  • Organizer: Infinite analysis 2914
  • Place of Presentation: 東京大学（東京都)
  • Invited
• [Presentation] Correlations in spin chains at finite temperature (2013)
  • Author(s): J. Suzuki
  • Organizer: Integrability & CFT (StatPhys サテライト)
  • Place of Presentation: 梨花女子大学（ソウル・韓国）
  • Invited
• [Presentation] Factorization of density matrix elements of higher spin chains at finite temperatures (2013)
  • Author(s): J. Suzuki
  • Organizer: Mathematical Statistical Physics
  • Place of Presentation: 京都大学（京都府)
  • Invited
• [Presentation] Quantum spin chains at arbitrary temperatures (2013)
  • Author(s): J. Suzuki
  • Organizer: Integrability in Quantum and Statistical Systems
  • Place of Presentation: 国立台湾大学（台北）
  • Invited
• [Presentation] Correlation functions of higher spin chains (2013)
  • Author(s): J. Suzuki
  • Organizer: Correlation functions of quantum integrable models
  • Place of Presentation: University of Burgourne(Dijon)
  • Invited