Action of the monodromy matrix entries in the generalized algebraic Bethe ansatz

TL;DR

This paper analyzes the action of monodromy matrix entries in the generalized algebraic Bethe ansatz for the XYZ spin chain, expressing these actions as linear combinations of Bethe vectors and linking results to the 8-vertex model.

Contribution

It provides explicit calculations of monodromy matrix actions on Bethe vectors within the generalized algebraic Bethe ansatz framework for the XYZ spin chain.

Findings

Derived explicit formulas for monodromy matrix actions on Bethe vectors.

Connected multiple actions to the partition function of the 8-vertex model.

Enhanced understanding of algebraic structures in integrable models.

Abstract

We consider an $XYZ$ spin chain within the framework of the generalized algebraic Bethe ansatz. We calculate the actions of monodromy matrix elements on Bethe vectors as a linear combination of new Bethe vectors. We also compute the multiple action of the gauge transformed monodromy matrix elements on the pre-Bethe vector and conceive the result in terms of a partition function of the 8-vertex model.