Integrable Spin Chains Associated to $\widehat{sl_q(n)}$ and $\widehat{sl_{p,q}(n)}$

TL;DR

This paper explores new integrable spin chain models derived from the quantum affine algebra $U_q(\, ext{hat}\,sl(n))$ and biparametric deformations, analyzing specific cases and solving for $n=3$ using nested Bethe ansatz.

Contribution

It introduces new integrable spin chain models associated with $\, ext{hat}\,sl(n)$ algebras and relates them to biparametric models, providing explicit solutions for $n=3$.

Findings

Derived new integrable models from the $U_q(\, ext{hat}\,sl(n))$ algebra.

Established the relation between these models and biparametric $\, ext{hat}\,sl_{p,q}(n)$ models.

Solved the $n=3$ case using nested Bethe ansatz and analyzed parameter dependence.

Abstract

The Hoft structure of the central extension of the $U_q \left( \widehat{sl\left( n \right) }\right)$ algebra is considered. The intertwine matrix induces new integrable spin chain models. We show the relation of these models and the biparametric spin chain $\widehat{sl_{p,q} \left( n \right)}$ models. The cases $n=2$ are $n=3$ are discussed and for $n=2$ we obtain the model of Dasgupta and Chowdhury . The case $n=3$ is solved with nested Bethe ansatz method and it is showed the dependence of the Bethe equations in the second parameter introduced