Algebraic Bethe ansatz for eight vertex model with general open-boundary conditions

TL;DR

This paper develops an algebraic Bethe ansatz approach for the eight vertex model with general open boundary conditions, including off-diagonal boundary matrices, expanding the solvable boundary conditions in integrable models.

Contribution

It introduces a method to derive Bethe ansatz equations for the eight vertex model with the most general open boundary conditions, including off-diagonal boundary matrices.

Findings

Derived Bethe ansatz equations for the eight vertex model with general open boundaries.

Extended the algebraic Bethe ansatz framework to models with off-diagonal boundary matrices.

Applicable to SOS models with reflection boundaries.

Abstract

By using the intertwiner and face-vertex correpondence relation, we obtain the Bethe ansatz equation of eight vertex model with open boundary condtitions in the framework of algebraic Bethe ansatz method. The open boundary condition under consideration is the general solution of the reflection equation for eight vertex model with only one restriction on the free parameters of the right side reflecting boundary matrix. The reflecting boundary matrices used in this paper thus may have off-diagonal elements. Our construction can also be used for the Bethe ansatz of SOS model with reflection boundaries.