INTEGRABLE SU(3) SPIN CHAIN COMBINING DIFFERENT REPRESENTATIONS

The general expression for the local matrix t(theta) of a quantum chai n 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 fulfilment of the Yang-Baxter equation. Then, a non-h omogeneous 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 calculate d.