The algebraic Bethe ansatz for open A_{2n}^{(2)} vertex model

TL;DR

This paper applies the algebraic Bethe ansatz to solve the open $A_{2n}^{(2)}$ vertex model with diagonal reflecting matrices, deriving eigenvalues and Bethe equations, and confirming results with quantum invariance cases.

Contribution

It introduces an algebraic Bethe ansatz approach for the $A_{2n}^{(2)}$ vertex model with diagonal boundaries, providing explicit eigenvalues and Bethe equations.

Findings

Derived eigenvalues of the transfer matrix.

Established Bethe ansatz equations for the model.

Confirmed results match analytic Bethe ansatz in quantum invariant cases.

Abstract

We solve the $A_{2n}^{(2)}$ vertex model with all kinds of diagonal reflecting matrices by using the algebraic Behe ansatz, which includes constructing the multi-particle states and achieving the eigenvalue of the transfer matrix and corresponding Bethe ansatz equations. When the model is $U_q(B_n)$ quantum invariant, our conclusion agrees with that obtained by analytic Bethe ansatz method.