Exact Bethe Ansatz solution for $A_{n-1}$ chains with non-$SU_{q}(n)$ invariant open boundary conditions

TL;DR

This paper extends the Nested Bethe Ansatz to solve $A_{n-1}$ vertex models and $SU(n)$ spin chains with general open boundary conditions, providing exact eigenvalues, eigenvectors, and finite size corrections.

Contribution

It introduces a generalized Bethe Ansatz for open boundaries with continuous and discrete parameters, covering all diagonal reflection solutions.

Findings

Exact eigenvalues and eigenvectors for $A_{n-1}$ chains with open boundaries.

Bethe ansatz equations for finite size corrections.

Comprehensive solution for all diagonal reflection boundary conditions.

Abstract

The Nested Bethe Ansatz is generalized to open and independent boundary conditions depending on two continuous and two discrete free parameters. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex models and $SU(n)$ spin chains with such boundary conditions. The solution is found for all diagonal families of solutions to the reflection equations in all possible combinations. The Bethe ansatz equations are used to find de first order finite size correction.