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

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

1996-09-24

arxiv.org/abs/cond-mat/9609228v1

Physics

Condensed Matter

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

Scientific paper

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.

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