J. Abad et M. Rios, INTEGRABLE SU(3) SPIN CHAIN COMBINING DIFFERENT REPRESENTATIONS, Journal of physics. A, mathematical and general, 30(17), 1997, pp. 5887-5909
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.