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Chinese Physics Letters

Exact Solution for Perk-Schultz Model with Boundary Impurities

Guang-Liang Li, Rui‐Hong Yue, Shi Kang-Jie, Bo-Yu Hou

Published Feb 8, 2001• 23 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/18/3/302

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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.
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.
We propose an integrable spin-1 chain with a magnetic impurity whose spin is 1/2.The integrability of the model is based on an operator solution of the associated reflection equation.Due to the existence of the impurity, the SU(3) symmetry of the bulk is broken.By using the nested algebraic Bethe ansatz, we obtain the exact solution of the system.The eigenvalues, eigenstates, and Bethe ansatz equations are given explicitly.The method provided in this paper can be generalized to other high-rank quantum integrable systems with magnetic impurities where the spins of the bulk and of impurities are different.
The exact solution of the one-dimensional super-symmetric t-J model under generic integrable boundary conditions is obtained via the Bethe ansatz methods. With the coordinate Bethe ansatz, the corresponding R-matrix and K-matrices are derived for the second eigenvalue problem associated with spin degrees of freedom. It is found that the second eigenvalue problem can be transformed to that of the transfer matrix of the inhomogeneous XXX spin chain, which allows us to obtain the spectrum of the Hamiltonian and the associated Bethe ansatz equations by the off-diagonal Bethe ansatz method.