Multiple reference states and complete spectrum of the $Z_n$ Belavin model with open boundaries

TL;DR

This paper uncovers multiple reference states in the $ ext{Z}_n$ Belavin model with open boundaries, revealing the full spectrum through $n$ eigenvalue sets and extending results to the Gaudin model in the classical limit.

Contribution

It introduces the existence of $n$ reference states for the $ ext{Z}_n$ Belavin model with non-diagonal boundaries, enabling the complete spectral characterization.

Findings

Identified $n$ reference states for the model.

Derived $n$ sets of eigenvalues and Bethe Ansatz equations.

Connected the spectrum to the Gaudin model in the classical limit.

Abstract

The multiple reference state structure of the $\Z_n$ Belavin model with non-diagonal boundary terms is discovered. It is found that there exist $n$ reference states, each of them yields a set of eigenvalues and Bethe Ansatz equations of the transfer matrix. These $n$ sets of eigenvalues together constitute the complete spectrum of the model. In the quasi-classic limit, they give the complete spectrum of the corresponding Gaudin model.