The spectrum of an open vertex model based on the U_q[SU(2)] at roots of unity

TL;DR

This paper provides an exact solution for an open vertex model based on the $U_q[SU(2)]$ algebra at roots of unity, revealing the structure of eigenvalues and Bethe ansatz equations with boundary effects.

Contribution

It introduces a class of diagonal $K$-matrices with a free parameter and derives the eigenvalues and Bethe ansatz equations for the model using algebraic Bethe ansatz.

Findings

Derived eigenvalues of the transfer matrix.

Formulated Bethe ansatz equations incorporating boundary parameters.

Identified the influence of roots of unity on scattering phases.

Abstract

We study the exact solution of an $N$-state vertex model based on the representation of the $U_q[SU(2)]$ algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal $K$-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables.