Integrable quantum chains combining site states in different representations of $su(3)$

Abstract

The general expression for the local matrix $L(\theta )$ of a quantum chain 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. Then, a non-homogeneous spin chain combining different representations of $su(3)$ is solved by 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.

Contribution presented in XXI Inter. Coll. on Group Theor. Methods, Goslar (1996), revtex, 4 figures