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Journal of Physics A Mathematical and General

Algebraic Bethe ansatz for integrable one-dimensional extended Hubbard models with open boundary conditions

Xiangyu Ge, M. D. Gould

Published Feb 5, 2003• 3 citations
Publisher

Abstract

Nine classes of integrable open boundary conditions, further extending the one-dimensional U q ( gl (2|2)) extended Hubbard model, have been constructed previously by means of the boundary Z 2 -graded quantum inverse scattering method. The boundary systems are now solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained for all nine cases.

DOI
10.1088/0305-4470/36/7/302

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Bulletin of the Australian Mathematical Society•Jun 1, 2001•0 citations
Nine classes of integrable open boundary conditions, further extending the one-dimensional U q ( gl (2|2)) extended Hubbard model, have been constructed previously by means of the boundary Z 2 -graded quantum inverse scattering method. The boundary systems are now solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained for all nine cases.
Three kinds of integrable Kondo problems in one-dimensional extended Hubbard models are studied by means of the boundary graded quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are presented as a nontrivial realization of the graded reflection equation algebras acting in a ${(2s}_{\ensuremath{\alpha}}+1)$-dimensional impurity Hilbert space. Furthermore, these models are solved using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.
Integrability of strongly correlated electron systems on open chains XIANG-YU GEIn recent years, there has been a strong increase of interest in models of strongly correlated electron systems in condensed matter physics, in particular in integrable onedimensional models.Examples of such models are the one-dimensional Hubbard model, the supersymmetric t-J model, the Hubbard-like model (Bariev's chain), the so-called extended Hubbard model (EKS model), the supersymmetric U model and the eight-state supersymmetric U model.The study of integrable open-boundary conditions for strongly correlated electron models is very important for physical applications, especially for gaining insights into the behaviour of more realistic systems.The important ingredient in Sklyanin's boundary quantum inverse scattering method (QISM), which has played a key role in recent advances in the study of lattice models with open-boundaries, is a new algebraic structure, the reflection equation algebra.In this thesis, a general graded reflection equation algebra is proposed and the corresponding graded (supersymmetry) boundary QISM is formulated.The formalism is applicable to all boundary lattice systems where an invertible i?-matrix exists.As applications, some important integrable boundary conditions for various strongly correlated electron models with quantum superalgebra symmetries are constructed, including:1. Presentation of integrable open-boundary conditions for the one-dimensional qdeformed supersymmetric Essler-Korepin-Schoutens (EKS) extended Hubbard model.Determination of three different diagonal boundary if-matrices and of nine classes of integrable open-boundary conditions.Construction of the exactly solvable Hamiltonian with open-boundary terms for quantum superalgebra U q (gl(2\2)) symmetry; 2. Establishment of the quantum integrability of open-boundary conditions for the one-dimensional ^-deformed supersymmetric U model with quantum superalgebra U q (gl(2\l)} symmetry.Determination of diagonal boundary if-matrices and of integrable open-boundary conditions.Solution of the boundary system by means of the coordinate space Bethe ansatz technique, and derivation of the Bethe ansatz equations;