The algebraic Bethe ansatz for open vertex models

TL;DR

This paper develops a unified algebraic Bethe ansatz approach for open vertex models associated with various Lie algebras, providing solutions for models with trivial and certain non-trivial boundary conditions, and confirming results with analytical methods.

Contribution

It introduces a unified algebraic Bethe ansatz framework for multiple open vertex models, including solutions with trivial and non-trivial boundary matrices, extending previous analytical results.

Findings

Successfully solved models with trivial K matrices

Extended solutions to models with non-trivial diagonal K matrices

Results agree with analytical Bethe ansatz methods

Abstract

We present a unified algebraic Bethe ansatz for open vertex models which are associated with the non-exceptional $A^{(2)}_{2n},A^{(2)}_{2n-1},B^{(1)}_n,C^{(1)}_n,D^{(1)}_{n}$ Lie algebras. By the method, we solve these models with the trivial K matrix and find that our results agree with that obtained by analytical Bethe ansatz. We also solve the $B^{(1)}_n,C^{(1)}_n,D^{(1)}_{n}$ models with some non-trivial diagonal K-matrices (one free parameter case) by the algebraic Bethe ansatz.