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Journal of Physics A Mathematical and General

The openXXZchain with boundary impurities

Shu Chen, Yupeng Wang, Fu‐Cho Pu

Published May 22, 1998• 9 citations
Publisher

Abstract

We propose an integrable open XXZ chain coupled to the boundary impurities with arbitrary exchange constants. The Bethe ansatz equation and eigenvalues are obtained by using the quantum inverse scattering method. The ground-state properties are discussed by solving the Bethe equation in some special cases. In addition, we present an approach for constructing the reflecting matrix K which produces the boundary term coupled to impurities.

DOI
10.1088/0305-4470/31/20/005

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We propose an integrable open XXZ chain coupled to the boundary impurities with arbitrary exchange constants. The Bethe ansatz equation and eigenvalues are obtained by using the quantum inverse scattering method. The ground-state properties are discussed by solving the Bethe equation in some special cases. In addition, we present an approach for constructing the reflecting matrix K which produces the boundary term coupled to impurities.
We review recent results on the Bethe Ansatz solutions for the eigenvalues of the transfer matrix of an integrable open XXZ quantum spin chain using functional relations which the transfer matrix obeys at roots of unity. First, we consider a case where at most two of the boundary parameters {{alpha−\\alpha_-alpha−​,alpha+\\alpha_+alpha+​,beta−\\beta_-beta−​,beta+\\beta_+beta+​}} are nonzero. A generalization of the Baxter T−QT-QT−Q equation that involves more than one independent QQQ is described. We use this solution to compute the boundary energy of the chain in the thermodynamic limit. We conclude the paper with a review of some results for the general integrable boundary terms, where all six boundary parameters are arbitrary.
Employing the graded versions of the Yang-Baxter equation and the reflection equations, we construct two kinds of integrable impurities for a small-polaron model with general open boundary conditions: (a) we shift the spectral parameter of the local Lax operator at arbitrary sites in the bulk and (b) we embed the impurity fermion vertex at each boundary of the chain. The Hamiltonians with different types of impurity terms are given explicitly. The Bethe ansatz equations, as well as the eigenvalues of the Hamiltonians, are constructed by means of the quantum inverse scattering method. In addition, we discuss the ground-state properties in the thermodynamic limit.