Thermodynamic limit of the XXZ central spin model with an arbitrary central magnetic field

doi:10.1088/1674-1056/acb426

中国物理B ›› 2023, Vol. 32 ›› Issue (9): 90307-090307.doi: 10.1088/1674-1056/acb426

Thermodynamic limit of the XXZ central spin model with an arbitrary central magnetic field

Fa-Kai Wen(温发楷)^1,2,3 and Kun Hao(郝昆)^4,5,6,†

1 College of Physics and Electronic Information, Yunnan Normal University, Kunming 650500, China;
2 Yunnan Key Laboratory of Opto-Electronic Information Technology, Kunming 650500, China;
3 State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;
4 Institute of Modern Physics, Northwest University, Xi'an 710127, 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:2022-11-02 修回日期:2022-12-29 接受日期:2023-01-18 发布日期:2023-08-28
通讯作者: Kun Hao E-mail:haoke72@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11847245, 11874393, and 12134015), the Doctoral Scientific Research Foundation of Yunnan Normal University (Grant No. 00900205020503180), the National Natural Science Foundation of China (Grant Nos. 12275214, 11805152, 12047502, and 11947301), the Natural Science Basic Research Program of Shaanxi Province (Grant Nos. 2021JCW-19 and 2019JQ-107), and the Shaanxi Key Laboratory for Theoretical Physics Frontiers in China.

Thermodynamic limit of the XXZ central spin model with an arbitrary central magnetic field

Fa-Kai Wen(温发楷)^1,2,3 and Kun Hao(郝昆)^4,5,6,†

1 College of Physics and Electronic Information, Yunnan Normal University, Kunming 650500, China;
2 Yunnan Key Laboratory of Opto-Electronic Information Technology, Kunming 650500, China;
3 State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;
4 Institute of Modern Physics, Northwest University, Xi'an 710127, 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:2022-11-02 Revised:2022-12-29 Accepted:2023-01-18 Published:2023-08-28
Contact: Kun Hao E-mail:haoke72@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11847245, 11874393, and 12134015), the Doctoral Scientific Research Foundation of Yunnan Normal University (Grant No. 00900205020503180), the National Natural Science Foundation of China (Grant Nos. 12275214, 11805152, 12047502, and 11947301), the Natural Science Basic Research Program of Shaanxi Province (Grant Nos. 2021JCW-19 and 2019JQ-107), and the Shaanxi Key Laboratory for Theoretical Physics Frontiers in China.

摘要/Abstract

摘要： The U(1) symmetry of the XXZ central spin model with an arbitrary central magnetic field B is broken, since its total spin in the z-direction is not conserved. We obtain the exact solutions of the system by using the off-diagonal Bethe ansatz method. The thermodynamic limit is investigated based on the solutions. We find that the contribution of the inhomogeneous term in the associated T-Q relation to the ground state energy satisfies an N^-1 scaling law, where N is the total number of spins. This result makes it possible to investigate the properties of the system in the thermodynamic limit. By assuming the structural form of the Bethe roots in the thermodynamic limit, we obtain the contribution of the direction of B to the ground state energy. It is shown that the contribution of the direction of the central magnetic field is a finite value in the thermodynamic limit. This is the phenomenon caused by the U(1) symmetry breaking of the system.

关键词: integrable spin chain, Bethe ansatz, T-Q relation, central spin model, thermodynamic limit

Abstract: The U(1) symmetry of the XXZ central spin model with an arbitrary central magnetic field B is broken, since its total spin in the z-direction is not conserved. We obtain the exact solutions of the system by using the off-diagonal Bethe ansatz method. The thermodynamic limit is investigated based on the solutions. We find that the contribution of the inhomogeneous term in the associated T-Q relation to the ground state energy satisfies an N^-1 scaling law, where N is the total number of spins. This result makes it possible to investigate the properties of the system in the thermodynamic limit. By assuming the structural form of the Bethe roots in the thermodynamic limit, we obtain the contribution of the direction of B to the ground state energy. It is shown that the contribution of the direction of the central magnetic field is a finite value in the thermodynamic limit. This is the phenomenon caused by the U(1) symmetry breaking of the system.

Key words: integrable spin chain, Bethe ansatz, T-Q relation, central spin model, thermodynamic limit

中图分类号: (Quantum information)

03.67.-a

02.30.Ik (Integrable systems) 75.10.Pq (Spin chain models) 42.50.Pq (Cavity quantum electrodynamics; micromasers)

Fa-Kai Wen(温发楷) and Kun Hao(郝昆). Thermodynamic limit of the XXZ central spin model with an arbitrary central magnetic field[J]. 中国物理B, 2023, 32(9): 90307-090307.

Fa-Kai Wen(温发楷) and Kun Hao(郝昆). Thermodynamic limit of the XXZ central spin model with an arbitrary central magnetic field[J]. Chin. Phys. B, 2023, 32(9): 90307-090307.

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Thermodynamic limit of the XXZ central spin model with an arbitrary central magnetic field

Thermodynamic limit of the XXZ central spin model with an arbitrary central magnetic field

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