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

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.

Automated summary

In this study, the exact solution of the Gaudin model with various interactions was examined using the off-diagonal Bethe ansatz method. The Bethe states of the model were constructed and the behavior of Bethe roots under U(1) symmetry recovery was observed. These findings lay the groundwork for further investigations into the thermodynamic limit, correlation functions, and quantum dynamics of the Gaudin model.