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arXiv:nlin/0407006 · Journal of Physics A Mathematical and General

Algebraic Bethe ansatz solutions for thesl(2|1)(2)andosp(2|1) models with boundary terms

V. Kurak, A. Lima-Santos

Published Mar 3, 2005• 9 citations
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Abstract

This work is concerned with the formulation of the graded quantum inverse scattering method for a class of lattice models with reflecting boundary conditions. The sl (2|1) (2) and osp (2|1) models are considered with their diagonal reflections in BFB grading. This allowed us to derive the eigenvalues and eigenvectors for the corresponding transfer matrices as well as explicit expressions for the Bethe ansatz equations.

DOI
10.1088/0305-4470/38/11/004

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This work is concerned with the formulation of the graded quantum inverse scattering method for a class of lattice models with reflecting boundary conditions. The sl (2|1) (2) and osp (2|1) models are considered with their diagonal reflections in BFB grading. This allowed us to derive the eigenvalues and eigenvectors for the corresponding transfer matrices as well as explicit expressions for the Bethe ansatz equations.
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The graded off-diagonal Bethe ansatz method is proposed to study supersymmetric quantum integrable models (i.e., quantum integrable models associated with superalgebras). As an example, the exact solutions of the SU(2|2) vertex model with both periodic and generic open boundary conditions are constructed. By generalizing the fusion techniques to the supersymmetric case, a closed set of operator product identities about the transfer matrices are derived, which allows us to give the eigenvalues in terms of homogeneous or inhomogeneous T−Q relations. The method and results provided in this paper can be generalized to other high rank supersymmetric quantum integrable models.