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Integrable boundary conditions for supersymmetric U model

Xiangyu Ge, Huan-Qiang Zhou

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

The integrable open-boundary conditions for the supersymmetric U model, which may be of relevance to high-T-C superconductivity,are considered. The diagonal boundary K-matrices are found and a class of integrable boundary terms are determined. Further, the boundary model Hamiltonians are solved by means of the coordinate Bethe ansatz method and the Bethe ansatz equations are derived.

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•Jan 1, 1999•0 citations
The integrable open-boundary conditions for the supersymmetric U model, which may be of relevance to high-T-C superconductivity,are considered. The diagonal boundary K-matrices are found and a class of integrable boundary terms are determined. Further, the boundary model Hamiltonians are solved by means of the coordinate Bethe ansatz method and the Bethe ansatz equations are derived.
Quantum integrability is established for the one-dimensional supersymmetric UUU model with boundary terms by means of the quantum inverse-scattering method. The boundary supersymmetric UUU chain is solved by using the coordinate-space Bethe-ansatz technique and Bethe-ansatz equations are derived. This provides us with a basis for computing the finite-size corrections to the low-lying energies in the system.
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;