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arXiv:hep-th/9604072 · Nuclear Physics B

One-parameter family of an integrable spl(2|1) vertex model: Algebraic Bethe ansatz and ground state structure

P B Ramos, Marcio Jose Martins

Published Sep 1, 1996• 64 citations
arXivHTMLPDF
DOI
10.1016/0550-3213(96)00342-2

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In this work we investigate the supersymmetric t-J model in one dimension. The spectrum of the hamiltonian is obtained by means of the algebraic nested Bethe-ansatz method. Furthermore, we present a detailed analysis of the algebraic structure of the states. By combining the Bethe ansatz with the spl(2,1) supersymmetry of the t-J hamiltonian a complete set of eigenstates is constructed. The ground state and the elementary excitations of the model are investigated. We also introduce a new integrable vertex model, the anisotropic t-J model, which possesses splq(2, 1) "quantum supergroup" invariance.
Given a family of monodromy matrices T0,T1,…,TK−1 corresponding to integrable anisotropic vertex models of Anμ−1 type, μ=0,1,…,K−1, we built up a related mixed vertex model by means of gluing the lattices on which they are defined, in such a way that integrability property is preserved. The gluing process is implemented through one-dimensional representations of rectangular quantum matrix algebras A(Rnμ−1:Rnμ), namely, the gluing matrices ζμ. Algebraic Bethe ansatz is applied on a pseudovacuum space with a selected basis and, for each element of this basis, it yields a set of nested Bethe ansatz equations matching up to the ones corresponding to an Am−1 quasiperiodic model, with m equal to minμ∈ZK{rank ζμ}.