Modified algebraic Bethe ansatz for XXZ chain on the segment - II - general cases

TL;DR

This paper develops a modified algebraic Bethe ansatz method to solve the spectral problem of the XXZ spin chain with general integrable boundary conditions, providing explicit eigenvalues and eigenvectors.

Contribution

It introduces a new approach to handle the most general boundary conditions in the XXZ chain within the algebraic Bethe ansatz framework, extending previous methods.

Findings

Eigenvalues and eigenvectors explicitly obtained.

Bethe roots satisfy modified Bethe equations with an additional term.

Applicable to the most general integrable boundary conditions.

Abstract

The spectral problem of the Heisenberg XXZ spin-$\frac{1}{2}$ chain on the segment is investigated within a modified algebraic Bethe ansatz framework. We consider in this work the most general boundaries allowed by integrability. The eigenvalues and the eigenvectors are obtained. They are characterised by a set of Bethe roots with cardinality equal to $N$, the length of the chain, and which satisfies a set of Bethe equations with an additional term.