Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9909258 · Modern Physics Letters B

INTEGRABLE BOUNDARY CONDITIONS FOR THE q-DEFORMED EXTENDED HUBBARD MODEL

Xiangyu Ge

Published Jun 30, 1999• 7 citations
arXivHTMLPDF

Abstract

Integrable open-boundary condition for the q-deformed Essler–Korepin–Schoutens extended Hubbard model of strongly correlated electrons are studied in the framework of the boundary quantum inverse scattering method. Diagonal boundary K-matrices are found and nine classes of integrable boundary terms are determined.
DOI
10.1142/s0217984999000634

Related papers

Integrability of strongly correlated electron systems on open chains

Xiangyu Ge

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;

Bulletin of the Australian Mathematical Society•Jun 1, 2001•0 citations

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

Xiangyu Ge, M. D. Gould

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.

Journal of Physics A Mathematical and General•Feb 5, 2003•3 citations

Integrable Boundary Conditions for the One-Dimensional Hubbard Model

Masahiro Shiroishi, Miki Wadati

We discuss the integrable boundary conditions for the one-dimensional (1D) Hubbard Model in the framework of the Quantum Inverse Scattering Method (QISM). We use the fermionic R-matrix proposed by Olmedilla et al. to treat the twisted periodic boundary condition and the open boundary condition. We determine the most general form of the integrable twisted periodic boundary condition by considering the symmetry matrix of the fermionic R-matrix. To find the integrable open boundary condition, we shall solve the graded reflection equation, and find there are two diagonal solutions, which correspond to a) the boundary chemical potential and b) the boundary magnetic field. Non-diagonal solutions are obtained using the symmetry matrix of the fermionic R-matrix and the covariance property of the graded reflection equation. They can be interpreted as the SO(4) rotations of the diagonal solutions.

arXiv:cond-mat/9708011•Journal of the Physical Society of Japan•Aug 15, 1997•62 citations

Integrable extended Hubbard models with boundary Kondo impurities

Anthony J. Bracken, Xiangyu Ge, M. D. Gould +1 more

Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z2-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

Bulletin of the Australian Mathematical Society•Dec 1, 2001•0 citations

On the Quantum Integrability for A Model of Coupled XY Chains

Huan-Qiang Zhou, Xiangyu Ge

The paper discusses integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of integrable boundary terms are determined. The boundary model Hamiltonian is solved by using the coordinate space Bethe ansatz technique and Bathe ansatz equations are derived.

•Jan 1, 1999•0 citations

EXACT SOLVING q DEFORMED BOSON MODEL UNDER OPEN BOUNDARY CONDITION

Bo Li, Yanshen Wang

Utilizing the algebraic Bethe–Ansatz method, the Hamiltonian of q deformed boson model and its eigenvalue equation are calculated under the integrable open boundary condition. Rely on them, we give the exact energy spectrum and discuss two limit cases of the model.

Modern Physics Letters B•Dec 13, 2011•4 citations
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;
We discuss the integrable boundary conditions for the one-dimensional (1D) Hubbard Model in the framework of the Quantum Inverse Scattering Method (QISM). We use the fermionic R-matrix proposed by Olmedilla et al. to treat the twisted periodic boundary condition and the open boundary condition. We determine the most general form of the integrable twisted periodic boundary condition by considering the symmetry matrix of the fermionic R-matrix. To find the integrable open boundary condition, we shall solve the graded reflection equation, and find there are two diagonal solutions, which correspond to a) the boundary chemical potential and b) the boundary magnetic field. Non-diagonal solutions are obtained using the symmetry matrix of the fermionic R-matrix and the covariance property of the graded reflection equation. They can be interpreted as the SO(4) rotations of the diagonal solutions.