Exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions

doi:10.1088/1674-1056/abcf43

中国物理B ›› 2021, Vol. 30 ›› Issue (5): 50201-050201.doi: 10.1088/1674-1056/abcf43

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Exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions

Fa-Kai Wen(温发楷)^1,† and Xin Zhang(张鑫)²

1 State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;
2 Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, 42097 Wuppertal, Germany

收稿日期:2020-08-31 修回日期:2020-10-24 接受日期:2020-12-01 出版日期:2021-05-14 发布日期:2021-05-14
通讯作者: Fa-Kai Wen E-mail:fakaiwen@wipm.ac.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11847245 and 11874393).

Exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions

Fa-Kai Wen(温发楷)^1,† and Xin Zhang(张鑫)²

1 State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;
2 Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, 42097 Wuppertal, Germany

Received:2020-08-31 Revised:2020-10-24 Accepted:2020-12-01 Online:2021-05-14 Published:2021-05-14
Contact: Fa-Kai Wen E-mail:fakaiwen@wipm.ac.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11847245 and 11874393).

摘要/Abstract

摘要： We study the exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions. The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method. Based on the off-diagonal Bethe ansatz solutions, we construct the Bethe states of the inhomogeneous XXX Heisenberg spin chain with the generic open boundaries. By taking a quasi-classical limit, we give explicit closed-form expression of the Bethe states of the Gaudin model. From the numerical simulations for the small-size system, it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1) symmetry. Furthermore, it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant. This fact enables us to recover the Bethe states of the Gaudin model with the U(1) symmetry. These results provide a basis for the further study of the thermodynamic limit, correlation functions, and quantum dynamics of the Gaudin model.

关键词: integrable models, Gaudin model, Bethe ansatz, Bethe states

Abstract: We study the exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions. The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method. Based on the off-diagonal Bethe ansatz solutions, we construct the Bethe states of the inhomogeneous XXX Heisenberg spin chain with the generic open boundaries. By taking a quasi-classical limit, we give explicit closed-form expression of the Bethe states of the Gaudin model. From the numerical simulations for the small-size system, it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1) symmetry. Furthermore, it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant. This fact enables us to recover the Bethe states of the Gaudin model with the U(1) symmetry. These results provide a basis for the further study of the thermodynamic limit, correlation functions, and quantum dynamics of the Gaudin model.

Key words: integrable models, Gaudin model, Bethe ansatz, Bethe states

中图分类号: (Integrable systems)

02.30.Ik

03.65.Fd (Algebraic methods) 04.20.Jb (Exact solutions) 75.10.Jm (Quantized spin models, including quantum spin frustration)

Fa-Kai Wen(温发楷) and Xin Zhang(张鑫). Exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions[J]. 中国物理B, 2021, 30(5): 50201-050201.

Fa-Kai Wen(温发楷) and Xin Zhang(张鑫). Exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions[J]. Chin. Phys. B, 2021, 30(5): 50201-050201.

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Exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions

Exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions

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