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

Integrable variant of the one-dimensional Hubbard model

X. -w. Guan, Angela Foerster, Jon Links, Huan-Qiang Zhou, Arlei Prestes Tonel, Ross H. McKenzie

Published Jan 1, 2001• 1 citation
OpenAlex

Abstract

Abstract. A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the new model possesses the SO(4) algebra symmetry, which contains a representation of the η-pairing SU(2) algebra and a spin SU(2) algebra. Additionally, the algebraic Bethe ansatz is studied by means of the quantum inverse scattering method. The spectrum of the Hamiltonian, eigenvectors, as well as the Bethe ansatz equations, are discussed. PACS numbers: 71.10.Fd, 71.10.Pm. Submitted to: J. Phys. A: Math. Gen. Integrable variant of the one-dimensional Hubbard model 2

Related papers

Integrable variant of the one-dimensional Hubbard model

X.-W. Guan, Angela Foerster, Jon Links +3 more

A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang–Baxter equation. We argue that the new model possesses the SO(4) algebra symmetry, which contains a representation of the η-pairing SU(2) algebra and a spin SU(2) algebra. Additionally, the algebraic Bethe ansatz is studied by means of the quantum inverse scattering method. The spectrum of the Hamiltonian, eigenvectors, as well as the Bethe ansatz equations, are discussed.

arXiv:cond-mat/0103059•Journal of Mathematical Physics•Jul 1, 2002•3 citations

New integrable 1D models of superconductivity

Marius de Leeuw, Anton Pribytok, Ana L. Retore +1 more

Abstract In this paper we find new integrable one-dimensional lattice models of electrons. We describe all such nearest-neighbour integrable models with s u ( 2 ) × s u ( 2 ) symmetry by classifying solutions of the Yang–Baxter equation following the procedure first introduced in [1]. We find 12 R-matrices of difference form, some of which can be related to known models such as the XXX spin chain and the free Hubbard model, and some are new models. In addition, integrable generalizations of the Hubbard model are found by keeping the kinetic term of the Hamiltonian and adding all terms which preserve fermion number. We find that most of the new models cannot be diagonalized using the standard nested Bethe Ansatz.

arXiv:1911.01439•Journal of Physics A Mathematical and Theoretical•Jul 22, 2020•25 citations

Fermionic R -Operator and Integrability of the One-Dimensional Hubbard Model

有希子 梅野, Masahiro Shiroishi, Miki Wadati

We propose a new type of the Yang-Baxter equation (YBE) and the decorated Yang-Baxter equation (DYBE). Those relations for the fermionic R-operator were introduced recently as a tool to treat the integrability of the fermion models. Using the YBE and the DYBE for the XX fermion model, we construct the fermionic R-operator for the one-dimensional (1D) Hubbard model. It gives another proof of the integrability of the 1D Hubbard model. Furthermore a new approach to the SO(4) symmetry of the 1D Hubbard model is discussed.

arXiv:cond-mat/9806144•Journal of the Physical Society of Japan•Jul 15, 1998•28 citations

Bethe Ansatz for theSU(4)Extension of the Hubbard Model

Heng Fan, Miki Wadati

We apply the nested algebraic Bethe ansatz method to solve the eigenvalue problem for the SU(4) extension of the Hubbard model. The Hamiltonian is equivalent to the SU(4) graded permutation operator. The graded Yang-Baxter equation and the graded Quantum Inverse Scattering Method are used to obtain the eigenvalue of the SU(4) extension of the Hubbard model.

arXiv:cond-mat/9911166•Journal of the Physical Society of Japan•Dec 15, 2000•2 citations

Bethe ansatz solutions of the 1D extended Hubbard-model

Haiyang Hou, Pei Sun, Yi Qiao +3 more

Abstract We construct an integrable 1D extended Hubbard model within the framework of the quantum inverse scattering method. With the help of the nested algebraic Bethe ansatz method, the eigenvalue Hamiltonian problem is solved by a set of Bethe ansatz equations, whose solutions are supposed to give the correct energy spectrum.

Communications in Theoretical Physics•Feb 22, 2024•1 citation

Scattering matrix and excitation spectrum of the Hubbard model

Fabian H.L. Eβler, V. E. Korepin

We consider the one-dimensional Hubbard model at half filling. We show that both excitation spectrum and S matrix are determined by the SO(4) symmetry of the model. The complete set of excitations is given by the scattering states of four elementary excitations, which form the fundamental representation of SU(2)\ifmmode\times\else\texttimes\fi{}SU(2). We evaluate the exact S matrix, which satisfies the Yang-Baxter relation. The results for the repulsive and attractive Hubbard model are related by an interchange of spin and charge degrees of freedom.

arXiv:cond-mat/9308004•Physical Review Letters•Feb 7, 1994•60 citations
Abstract. A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the new model possesses the SO(4) algebra symmetry, which contains a representation of the η-pairing SU(2) algebra and a spin SU(2) algebra. Additionally, the algebraic Bethe ansatz is studied by means of the quantum inverse scattering method. The spectrum of the Hamiltonian, eigenvectors, as well as the Bethe ansatz equations, are discussed. PACS numbers: 71.10.Fd, 71.10.Pm. Submitted to: J. Phys. A: Math. Gen. Integrable variant of the one-dimensional Hubbard model 2
A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang–Baxter equation. We argue that the new model possesses the SO(4) algebra symmetry, which contains a representation of the η-pairing SU(2) algebra and a spin SU(2) algebra. Additionally, the algebraic Bethe ansatz is studied by means of the quantum inverse scattering method. The spectrum of the Hamiltonian, eigenvectors, as well as the Bethe ansatz equations, are discussed.
Abstract In this paper we find new integrable one-dimensional lattice models of electrons. We describe all such nearest-neighbour integrable models with s u ( 2 ) × s u ( 2 ) symmetry by classifying solutions of the Yang–Baxter equation following the procedure first introduced in [1]. We find 12 R-matrices of difference form, some of which can be related to known models such as the XXX spin chain and the free Hubbard model, and some are new models. In addition, integrable generalizations of the Hubbard model are found by keeping the kinetic term of the Hamiltonian and adding all terms which preserve fermion number. We find that most of the new models cannot be diagonalized using the standard nested Bethe Ansatz.
We propose a new type of the Yang-Baxter equation (YBE) and the decorated Yang-Baxter equation (DYBE). Those relations for the fermionic R-operator were introduced recently as a tool to treat the integrability of the fermion models. Using the YBE and the DYBE for the XX fermion model, we construct the fermionic R-operator for the one-dimensional (1D) Hubbard model. It gives another proof of the integrability of the 1D Hubbard model. Furthermore a new approach to the SO(4) symmetry of the 1D Hubbard model is discussed.
We consider the one-dimensional Hubbard model at half filling. We show that both excitation spectrum and S matrix are determined by the SO(4) symmetry of the model. The complete set of excitations is given by the scattering states of four elementary excitations, which form the fundamental representation of SU(2)\ifmmode\times\else\texttimes\fi{}SU(2). We evaluate the exact S matrix, which satisfies the Yang-Baxter relation. The results for the repulsive and attractive Hubbard model are related by an interchange of spin and charge degrees of freedom.