Exact solution of the $A^{(1)}_{n-1}$ trigonometric vertex model with non-diagonal open boundaries

TL;DR

This paper provides an exact algebraic Bethe ansatz solution for the $A^{(1)}_{n-1}$ trigonometric vertex model with non-diagonal open boundaries, deriving eigenvalues and Bethe equations.

Contribution

It introduces a novel algebraic Bethe ansatz approach for non-diagonal boundary conditions in the $A^{(1)}_{n-1}$ model, expanding solvable boundary cases.

Findings

Eigenvalues of the transfer matrix are explicitly obtained.

Bethe ansatz equations are derived for the model.

The method uses intertwiner and face-vertex relations.

Abstract

The $A^{(1)}_{n-1}$ trigonometric vertex model with {\it generic non-diagonal} boundaries is studied. The double-row transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the corresponding face-vertex relation. The eigenvalues and the corresponding Bethe ansatz equations are obtained.