Bethe Ansatze for 19-vertex Models

TL;DR

This paper analyzes the spectrum of 19-vertex quantum spin chains using Coordinate and Algebraic Bethe Ansatz methods, providing explicit eigenvalues and eigenvectors for models with periodic boundary conditions.

Contribution

It introduces a parametrization of wavefunctions and applies both Bethe Ansatz techniques to solve for the spectrum of specific 19-vertex models.

Findings

Spectrum of the models determined

Eigenvalues and eigenvectors explicitly obtained

Applicable to models with periodic boundary conditions

Abstract

The nineteen-vertex models of Zamolodchikov-Fateev, Izergin-Korepin and the supersymmetric osp(1|2) with periodic boundary conditions are studied. We find the spectrum of these quantum spin chains using the Coordinate Bethe Ansatz. The approche is a suitable parametrization of their wavefunctions. We also applied the Algebraic Bethe Ansatz in order to obtain the eigenvalues and eigenvectors of the corresponding transfer matrices.