中国物理B ›› 2023, Vol. 32 ›› Issue (11): 117504-117504.doi: 10.1088/1674-1056/ad0774

所属专题： SPECIAL TOPIC — Celebrating the 100th Anniversary of Physics Discipline of Northwest University

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Off-diagonal approach to the exact solution of quantum integrable systems

Yi Qiao(乔艺)1, Junpeng Cao(曹俊鹏)2,3,4,5,†, Wen-Li Yang(杨文力)1,5,6,‡, Kangjie Shi(石康杰)1, and Yupeng Wang(王玉鹏)2,5   

  1. 1 Institute of Modern Physics, Northwest University, Xi'an 710127, China;
    2 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
    3 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
    4 Songshan Lake Materials Laboratory, Dongguan 523808, China;
    5 Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China;
    6 Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
  • 收稿日期:2023-09-05 修回日期:2023-10-19 接受日期:2023-10-27 出版日期:2023-10-16 发布日期:2023-11-03
  • 通讯作者: Junpeng Cao, Wen-Li Yang E-mail:junpengcao@iphy.ac.cn;wlyang@nwu.edu.cn
  • 基金资助:
    Project supported by the National Key R&D Program of China (Grant No. 2021YFA1402104), the National Natural Science Foundation of China (Grant Nos. 12247103, 12305005, 12074410, 11934015, and 11975183), Major Basic Research Program of Natural Science of Shaanxi Province (Grant Nos. 2021JCW-19 and 2017ZDJC-32), Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33000000), Young Talent Fund of Xi’an Association for Science and Technology (Grant No. 959202313086), and Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 22JSZ005).

Off-diagonal approach to the exact solution of quantum integrable systems

Yi Qiao(乔艺)1, Junpeng Cao(曹俊鹏)2,3,4,5,†, Wen-Li Yang(杨文力)1,5,6,‡, Kangjie Shi(石康杰)1, and Yupeng Wang(王玉鹏)2,5   

  1. 1 Institute of Modern Physics, Northwest University, Xi'an 710127, China;
    2 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
    3 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
    4 Songshan Lake Materials Laboratory, Dongguan 523808, China;
    5 Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China;
    6 Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
  • Received:2023-09-05 Revised:2023-10-19 Accepted:2023-10-27 Online:2023-10-16 Published:2023-11-03
  • Contact: Junpeng Cao, Wen-Li Yang E-mail:junpengcao@iphy.ac.cn;wlyang@nwu.edu.cn
  • Supported by:
    Project supported by the National Key R&D Program of China (Grant No. 2021YFA1402104), the National Natural Science Foundation of China (Grant Nos. 12247103, 12305005, 12074410, 11934015, and 11975183), Major Basic Research Program of Natural Science of Shaanxi Province (Grant Nos. 2021JCW-19 and 2017ZDJC-32), Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33000000), Young Talent Fund of Xi’an Association for Science and Technology (Grant No. 959202313086), and Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 22JSZ005).

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摘要： We investigate the t-W scheme for the anti-ferromagnetic XXX spin chain under both periodic and open boundary conditions. We propose a new parametrization of the eigenvalues of the transfer matrix. Based on it, we obtain the exact solution of the system. By analyzing the distribution of zero roots at the ground state, we obtain the explicit expressions of the eigenfunctions of the transfer matrix and the associated $\mathbb{W}$ operator (see Eqs. (10) and (70)) in the thermodynamic limit. We find that the ratio of the quantum determinant with the eigenvalue of $\mathbb{W}$ operator for the ground state exhibits exponential decay behavior. Thus this fact ensures that the so-called inversion relation (the t-W relation without the W-term) can be used to study the ground state properties of quantum integrable systems with/without U(1)-symmetry in the thermodynamic limit.

关键词: quantum spin chain, bethe ansatz, Yang-Baxter equation

Abstract: We investigate the t-W scheme for the anti-ferromagnetic XXX spin chain under both periodic and open boundary conditions. We propose a new parametrization of the eigenvalues of the transfer matrix. Based on it, we obtain the exact solution of the system. By analyzing the distribution of zero roots at the ground state, we obtain the explicit expressions of the eigenfunctions of the transfer matrix and the associated $\mathbb{W}$ operator (see Eqs. (10) and (70)) in the thermodynamic limit. We find that the ratio of the quantum determinant with the eigenvalue of $\mathbb{W}$ operator for the ground state exhibits exponential decay behavior. Thus this fact ensures that the so-called inversion relation (the t-W relation without the W-term) can be used to study the ground state properties of quantum integrable systems with/without U(1)-symmetry in the thermodynamic limit.

Key words: quantum spin chain, bethe ansatz, Yang-Baxter equation

中图分类号:  (Spin chain models)

  • 75.10.Pq
02.30.Ik (Integrable systems) 03.65.Vf (Phases: geometric; dynamic or topological)