Integrable su(3) spin chain combining different representations

TL;DR

This paper develops a method to analyze integrable su(3) spin chains with sites in different representations, providing eigenvalue solutions via coupled Bethe equations and exploring the thermodynamic limit.

Contribution

It generalizes the transfer matrix for su(3) to arbitrary representations and introduces a nested Bethe ansatz approach for non-homogeneous chains.

Findings

Eigenvalues expressed as coupled Bethe equations

Solution for the thermodynamic limit of the ground state

Conjecture for chains with mixed su(n) representations

Abstract

The general expression for the local matrix $t(\theta)$ of a quantum chain with the site space in any representation of su(3) is obtained. This is made by generalizing $t(\theta)$ from the fundamental representation and imposing the fulfillment of the Yang-Baxter equation. Then, a non-homogeneous spin chain combining different representations of su(3) is solved by developing a method inspired in the nested Bethe ansatz. The solution for the eigenvalues of the trace of the monodromy matrix is given as two coupled Bethe equations. A conjecture about the solution of a chain with the site states in different representations of su(n) is presented. The thermodynamic limit of the ground state is calculated.