Nested Bethe ansatz for Y(gl(n)) open spin chains with diagonal boundary conditions

TL;DR

This paper develops a nested Bethe ansatz method for open XXX-type spin chains with arbitrary site representations and diagonal boundary conditions, providing eigenvalues, Bethe equations, and Bethe vectors.

Contribution

It introduces a generalized nested Bethe ansatz framework for open spin chains with arbitrary spins and diagonal boundaries, including trace formula expressions for Bethe vectors.

Findings

Derived eigenvalues and Bethe equations for the model

Provided explicit Bethe vector constructions using trace formulas

Extended Bethe ansatz applicability to general boundary matrices

Abstract

In this proceeding we present the nested Bethe ansatz for open spin chains of XXX-type, with arbitrary representations (i.e. `spins') on each site of the chain and diagonal boundary matrices $(K^+(u),K^-(u))$. The nested Bethe anstaz applies for a general $K^-(u)$, but a particular form of the $K^+(u)$ matrix. We give the eigenvalues, Bethe equations and the form of the Bethe vectors for the corresponding models. The Bethe vectors are expressed using a trace formula.