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/9907474 · Journal of the Physical Society of Japan

FermionicR-Operator Approach for the Small-Polaron Model with Open Boundary Condition

Yukiko Umeno, Heng Fan, Miki Wadati

Published Dec 15, 1999• 6 citations
arXivHTMLPDF

Abstract

Exact integrability and algebraic Bethe ansatz of the small-polaron model with the open boundary condition are discussed in the framework of the quantum inverse scattering method (QISM). We employ a new approach where the fermionic R-operator which consists of fermion operators is a key object. It satisfies the Yang-Baxter equation and the reflection equation with its corresponding K-operator. Two kinds of 'super-transposition' for the fermion operators are defined and the dual reflection equation is obtained. These equations prove the integrability and the Bethe ansatz equation which agrees with the one obtained from the graded Yang-Baxter equation and the graded reflection equations.

DOI
10.1143/jpsj.68.3826

Related papers

Bethe ansatz for the one-dimensional small-polaron model with open boundary conditions

Heng Fan, Xi‐Wen Guan

The one-dimensional small-polaron model with open boundary conditions is considered in the framework of the quantum inverse scattering method. The spin model which is equivalent to the small-polaron model is the Heisenberg $XXZ$ spin chain in an external magnetic field. For spin model, the solutions of the reflection equation (RE) and the dual RE are obtained. The eigenvalues and eigenvectors problems are solved by using the algebraic Bethe ansatz method. The case of the fermion model is also studied, the commuting of the transfer matrix can be proved, and the eigenvalues and the Bethe ansatz equations for fermion model are obtained.

arXiv:cond-mat/9711150•Nov 16, 1997•1 citation

Bethe Ansatz for the One-Dimensional Small-Polaron Model with Open Boundary Conditions

Xiao-Man Wang, Heng Fan, Xi‐Wen Guan

The one-dimensional small-polaron model with open boundary conditions is considered in the framework of the quantum inverse scattering method. The spin model which is equivalent to the small-polaron model is the Heisenberg X X Z spin chain in an external magnetic field. For spin model, the solutions of the reflection equation (RE) and the dual RE are obtained. The eigenvalues and eigenvectors problems are solved by using the algebraic Bethe ansatz method. The case of the fermion model is also studied, the commuting of the transfer matrix can be proved, and the eigenvalues and the Bethe ansatz equations for fermion model are obtained.

Journal of the Physical Society of Japan•Jan 1, 2000•3 citations

Integrable impurities for an open fermion chain

Xi‐Wen Guan, Uwe Grimm, Rudolf A. Römer +1 more

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.

arXiv:nlin/0001040•Journal of Physics A Mathematical and General•May 18, 2000•26 citations

FermionicR-Operator for the Fermion Chain Model

有希子 梅野, Masahiro Shiroishi, Miki Wadati

The integrability of the one-dimensional (1D) fermion chain model is investigated in the framework of the Quantum Inverse Scattering Method (QISM). We introduce a new R-operator for the fermion chain model, which is expressed in terms of the fermion operators. The R-operator satisfies a new type of the Yang-Baxter relation with fermionic L-operator. We derive the fermionic Sutherland equation from the relation, which is equivalent to the fermionic Lax equation. It also provides a mathematical foundation of the boost operator approach for the fermion model. In fact, we obtain some higher conserved quantities of the fermion model using the boost operator.

arXiv:hep-th/9806083•Journal of the Physical Society of Japan•Jun 15, 1998•21 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

Supersymmetric Extension of the Reflection Equation Algebra and Integrable Boundary Conditions in Doped Spin-1 Model

Xiangyu Ge, Miki Wadati

The reflection equation algebra of Sklyanin is extended to the supersymmetric case. A graded reflection equation algebra is proposed and the corresponding graded (supersymmetric) boundary quantum inverse scattering method (QISM) is formulated. As an application, integrable open-boundary conditions for the doped spin-1 chain of the supersymmetric t – J model are studied in the framework of the boundary QISM. Diagonal boundary K -matrices are found and four classes of integrable boundary terms are determined.

Journal of the Physical Society of Japan•Dec 11, 2006•0 citations
Exact integrability and algebraic Bethe ansatz of the small-polaron model with the open boundary condition are discussed in the framework of the quantum inverse scattering method (QISM). We employ a new approach where the fermionic R-operator which consists of fermion operators is a key object. It satisfies the Yang-Baxter equation and the reflection equation with its corresponding K-operator. Two kinds of 'super-transposition' for the fermion operators are defined and the dual reflection equation is obtained. These equations prove the integrability and the Bethe ansatz equation which agrees with the one obtained from the graded Yang-Baxter equation and the graded reflection equations.
The one-dimensional small-polaron model with open boundary conditions is considered in the framework of the quantum inverse scattering method. The spin model which is equivalent to the small-polaron model is the Heisenberg XXZXXZXXZ spin chain in an external magnetic field. For spin model, the solutions of the reflection equation (RE) and the dual RE are obtained. The eigenvalues and eigenvectors problems are solved by using the algebraic Bethe ansatz method. The case of the fermion model is also studied, the commuting of the transfer matrix can be proved, and the eigenvalues and the Bethe ansatz equations for fermion model are obtained.
The one-dimensional small-polaron model with open boundary conditions is considered in the framework of the quantum inverse scattering method. The spin model which is equivalent to the small-polaron model is the Heisenberg X X Z spin chain in an external magnetic field. For spin model, the solutions of the reflection equation (RE) and the dual RE are obtained. The eigenvalues and eigenvectors problems are solved by using the algebraic Bethe ansatz method. The case of the fermion model is also studied, the commuting of the transfer matrix can be proved, and the eigenvalues and the Bethe ansatz equations for fermion model are obtained.
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.
The integrability of the one-dimensional (1D) fermion chain model is investigated in the framework of the Quantum Inverse Scattering Method (QISM). We introduce a new R-operator for the fermion chain model, which is expressed in terms of the fermion operators. The R-operator satisfies a new type of the Yang-Baxter relation with fermionic L-operator. We derive the fermionic Sutherland equation from the relation, which is equivalent to the fermionic Lax equation. It also provides a mathematical foundation of the boost operator approach for the fermion model. In fact, we obtain some higher conserved quantities of the fermion model using the boost operator.
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.
The reflection equation algebra of Sklyanin is extended to the supersymmetric case. A graded reflection equation algebra is proposed and the corresponding graded (supersymmetric) boundary quantum inverse scattering method (QISM) is formulated. As an application, integrable open-boundary conditions for the doped spin-1 chain of the supersymmetric t – J model are studied in the framework of the boundary QISM. Diagonal boundary K -matrices are found and four classes of integrable boundary terms are determined.