Integrable su(3) spin chain combining different representations

The general expression for the local matrix $t(θ)$ of a quantum chain with the site space in any representation of su(3) is obtained. This is made by generalizing $t(θ)$ 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.

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