Gaudin Hypothesis for the XYZ Spin Chain

TL;DR

This paper verifies the Gaudin hypothesis for the XYZ spin chain by calculating the sum of Bethe vector norms and expressing it as a Jacobian within the algebraic Bethe ansatz framework.

Contribution

It provides a rigorous computation of Bethe vector norms for the XYZ spin chain, confirming the Gaudin hypothesis in this context.

Findings

Sum of Bethe vector norms expressed as a Jacobian

Confirmation of the Gaudin hypothesis for the XYZ spin chain

Application of algebraic Bethe ansatz to XYZ model

Abstract

The XYZ spin chain is considered in the framework of the generalized algebraic Bethe ansatz developed by Takhtajan and Faddeev. The sum of norms of the Bethe vectors is computed and expressed in the form of a Jacobian. This result corresponds to the Gaudin hypothesis for the XYZ spin chain.