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arXiv:cond-mat/9906083 · Physical review. B, Condensed matter

Exact diagonalization of the generalized supersymmetric t−J model with boundaries

Heng Fan, Miki Wadati, Xiaoman Wang

Published Feb 1, 2000• 17 citations
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Abstract

We study the generalized supersymmetric $t\ensuremath{-}J$ model with boundaries in three different gradings: fermionic, fermionic, bosonic (FFB), bosonic, fermionic, fermionic (BFF), and fermionic, bosonic, fermionic (FBF). Starting from the trigonometric R matrix, and in the framework of the graded quantum inverse scattering method, we solve the eigenvalue problems for the supersymmetric $t\ensuremath{-}J$ model. Detailed calculations are presented to obtain the eigenvalues and Bethe ansatz equations of the supersymmetric $t\ensuremath{-}J$ model with boundaries in three different backgrounds.

DOI
10.1103/physrevb.61.3450

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We study the generalized supersymmetric t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model with boundaries in three different gradings: fermionic, fermionic, bosonic (FFB), bosonic, fermionic, fermionic (BFF), and fermionic, bosonic, fermionic (FBF). Starting from the trigonometric R matrix, and in the framework of the graded quantum inverse scattering method, we solve the eigenvalue problems for the supersymmetric t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model. Detailed calculations are presented to obtain the eigenvalues and Bethe ansatz equations of the supersymmetric t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model with boundaries in three different backgrounds.
We study a one-dimensional model of free fermions with supersymmetry and demonstrate how non-diagonal boundary conditions can be incorporated into the framework of the graded quantum inverse scattering method (gQISM) by means of super matrices with entries from a superalgebra. For super Hermitian twists and open boundary conditions subject to a certain constraint, we solve the eigenvalue problem for the super transfermatrix by means of the graded algebraic Bethe ansatz technique (gABA) starting from a fermionic coherent state. For generic boundary conditions the algebraic Bethe ansatz cannot be applied. In this case the spectrum of the super transfermatrix is obtained from a functional relation.
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.