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
复制标题
具有 Dzyaloshinsky-Moriya 和 Kaplan-Shekhtman-Entin-Wohlman-Aharony 相互作用的 Gaudin 模型的精确解
DOI：
10.1088/1674-1056/abcf43
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发表时间：
2021
影响因子：
1.7
通讯作者：
Zhang Xin
中科院分区：
文献类型：
--
作者：
Wen Fa-Kai;Zhang Xin
我们研究了具有 Dzyaloshinsky-Moriya 和 Kaplan-Shekhtman-Entin-Wohlman-Aharony 相互作用的 Gaudin 模型的精确解。 Gaudin模型的能量方程和Bethe ansatz方程可以通过非对角Bethe ansatz方法得到。基于非对角 Bethe ansatz 解，我们构造了具有通用开放边界的非齐次 XXX Heisenberg 自旋链的 Bethe 态。通过取准经典极限，我们给出了高丁模型的 Bethe 态的显式封闭式表达式。对小尺寸系统的数值模拟表明，当Gaudin模型恢复U(1)对称性时，一些Bethe根趋于无穷大。此外，发现这些贝特根对贝特态的贡献是一个非零常数。这一事实使我们能够恢复具有 U (1) 对称性的 Gaudin 模型的 Bethe 状态。这些结果为进一步研究高丁模型的热力学极限、相关函数和量子动力学提供了基础。
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.