Algebraic Bethe Ansatz for gl(2,1) Invariant 36-Vertex Models

TL;DR

This paper applies the algebraic Bethe ansatz to compute spectra of transfer matrices for gl(2,1) invariant 36-vertex models, incorporating a free parameter in the representations.

Contribution

It introduces a generalized fusion procedure combined with nested algebraic Bethe ansatz for gl(2,1) models with free parameters.

Findings

Spectra of transfer matrices explicitly computed.

Method accommodates four-dimensional irreducible representations with free parameters.

Enhanced understanding of integrable models with superalgebra symmetry.

Abstract

Four dimensional irreducible representations of the superalgebra gl(2,1) carry a free parameter. We compute the spectra of the corresponding transfer matrices by means of the nested algebraic Bethe ansatz together with a generalized fusion procedure.