Bethe ansatz equations for quantum chains combining different representations of $su(3)$

TL;DR

This paper derives Bethe ansatz equations for quantum chains with sites in arbitrary $su(3)$ representations, extending previous models by generalizing the local L-matrix and applying a nested Bethe ansatz.

Contribution

It provides a general expression for the local L-matrix for any $su(3)$ representation and derives Bethe equations for chains combining two arbitrary $su(3)$ representations.

Findings

Derived Bethe equations for mixed $su(3)$ representations

Generalized the L-matrix for arbitrary $su(3)$ representations

Extended nested Bethe ansatz to multistate chains

Abstract

The general expression for the local matrix of a quantum chain $L(\theta)$ with the site space in any representation of $su(3)$ is obtained. This is made by generalizing $L(\theta)$ from the fundamental representation and imposing the fulfilment of the Yang-Baxter equation. With these operators and using a generalization of the nested Bethe ansatz, the Bethe equations for a multistate quantum chain combining two arbitrary representations of $su(3)$ are obtained .