A method for solve integrable $A_2$ spin chains combining different representations

Abstract

A non homogeneous spin chain in the representations $\{3\}$ and $\{3^{\ast }\}$ 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. PACS: 75.10.Jm, 05.50+q 02.20 Sv

PlainTeX, harvmac, 13 pages, 3 figures, to appear in Phys. Rev. B

References in corpus (4)

• Quantum Inverse Scattering Method and Correlation Functions
• Thermodynamics of Integrable Chains with Alternating Spins
• Scalar Kinks
• The class of universality of integrable and isotropic GL(N) mixed magnets

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