arXiv:cond-mat/9706136 · Journal of Physics A Mathematical and General

Integrable su(3) spin chain combining different representations

J. Abad, M Rios

Published Sep 7, 1997• 22 citations

Abstract

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

DOI: 10.1088/0305-4470/30/17/003

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arXiv:cond-mat/9706136 · Journal of Physics A Mathematical and General

Integrable su(3) spin chain combining different representations

J. Abad, M Rios

Published Sep 7, 1997• 22 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/0305-4470/30/17/003

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

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Integrable quantum chains combining site states in different representations of

su(3)

The general expression for the local matrix

L(θ)

of a quantum chain with the site space in any representation of

su(3)

is obtained. This is made by generalizing

L(θ)

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.

A nonhomogeneous spin chain in the representations {3} and {

{3}^{*}

} of

{A}_{2}

is analyzed. We find that the naive nested Bethe ansatz is not applicable to this case. A method inspired in the nested Bethe ansatz that can be applied to more general cases is developed for that chain. The solution for the eigenvalues of the trace of the monodromy matrix is given as two coupled Bethe equations different from that for a homogeneous chain. A conjecture about the form of the solutions for more general chains is presented.