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arXiv:cond-mat/9906409 · Journal of Physics A Mathematical and General

Boundary impurities in the generalized supersymmetrict-Jmodel

Heng Fan, Miki Wadati, Rui-hong Yue

Published Aug 25, 2000• 10 citations
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Abstract

We study the generalized supersymmetric t - J model with impurities in the boundaries. We first construct the higher spin operator K -matrix for the XXZ Heisenberg chain. Setting the boundary parameter to be a special value, we find a higher spin reflecting K -matrix for the supersymmetric t - J model. By using the quantum inverse scattering method, we obtain the eigenvalue and the corresponding Bethe ansatz equations.

DOI
10.1088/0305-4470/33/35/307

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We study the generalized supersymmetric t - J model with impurities in the boundaries. We first construct the higher spin operator K -matrix for the XXZ Heisenberg chain. Setting the boundary parameter to be a special value, we find a higher spin reflecting K -matrix for the supersymmetric t - J model. By using the quantum inverse scattering method, we obtain the eigenvalue and the corresponding Bethe ansatz equations.
The Perk-Schultz model with SU q ( m | n ) spin boundary impurities is constructed by dressing the c -number reflecting K -matrix with the local L -matrix which acts non-trivially on an impurity Hilbert space. The eigenvalue of the transfer matrix and the corresponding Bethe ansatz equations with different c -number reflecting K -matrices are obtained by using the nested Bethe ansatz method ( m ≠ n ). When m = 1, n = 2, our results come back to that of supersymmetric t - J model with SU q (1|2) spin boundary impurities.
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.
Integrable Kondo impurities in the one-dimensional supersymmetric U model of strongly correlated electrons are studied by means of the boundary graded quantum inverse scattering method. The boundary K -matrices depending on the local magnetic moments of the impurities are presented as non-trivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, the model Hamiltonian is diagonalized and the Bethe ansatz equations are derived. It is interesting to note that our model exhibits a free parameter in the bulk Hamiltonian but no free parameter exists on the boundaries. This is in sharp contrast to the impurity models arising from the supersymmetric t-J and extended Hubbard models where there is no free parameter in the bulk but there is a free parameter on each boundary.