Algebraic Bethe ansatz for 19-vertex models with upper triangular K-matrices

TL;DR

This paper applies the algebraic Bethe ansatz to solve 19-vertex models with non-diagonal, upper triangular boundary conditions, deriving eigenvalues and Bethe equations for these integrable systems.

Contribution

It introduces a method to diagonalize transfer matrices of 19-vertex models with non-diagonal upper triangular boundary matrices using generalized Bethe vectors.

Findings

Eigenvalues of the transfer matrix are explicitly derived.

Bethe equations characterizing the spectrum are obtained.

The approach extends Bethe ansatz techniques to models with non-diagonal boundaries.

Abstract

By means of an algebraic Bethe ansatz approach we study the Zamolodchikov-Fateev and Izergin-Korepin vertex models with non-diagonal boundaries, characterized by reflection matrices with an upper triangular form. Generalized Bethe vectors are used to diagonalize the associated transfer matrix. The eigenvalues as well as the Bethe equations are presented.