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/9812317 · Journal of Physics A Mathematical and General

Bethe Ansatz solution of a new class of Hubbard-type models

Andreas Osterloh, Luigi Amico A, Ulrich Eckern

Published Feb 28, 2000• 18 citations
arXivHTMLPDF

Abstract

We define one-dimensional particles with generalized exchange statistics. The exact solution of a Hubbard-type Hamiltonian constructed with such particles is achieved using the coordinate Bethe Ansatz. The chosen deformation of the statistics is equivalent to the presence of a magnetic field produced by the particles themselves, which is also present in a `free gas' of these particles.

DOI
10.1088/0305-4470/33/9/101

Related papers

Bethe Ansatz solution of a new class of Hubbard-type models

Andreas Osterloh

We define one-dimensional particles with generalized exchange statistics. The exact solution of a Hubbard-type Hamiltonian constructed with such particles is achieved using the coordinate Bethe Ansatz. The chosen deformation of the statistics is equivalent to the presence of a magnetic field produced by the particles themselves, which is also present in a `free gas' of these particles.

•Jan 1, 2000•9 citations

Exact Solution of a New Class of Bariev Model

Like Cao, Ke San-Min, Rui‐Hong Yue

The exact solution of a new type of Bariev Hamiltonian constructed with particles which obeys generalized exchange statistics in one dimension is studied in the framework of coordinate Bethe ansatz method. The energy spectrum and the related Bethe ansatz equations are obtained.

Communications in Theoretical Physics•Mar 1, 2007•0 citations

One-dimensional XXZ model for particles obeying fractional statistics

Luigi Amico A, Andreas Osterloh, Ulrich Eckern

We define one-dimensional particles as non-Abelian representations of the symmetric group ${S}_{N}.$ The exact solution of an $\mathrm{XXZ}$ type Hamiltonian built up with such particles is achieved using the coordinate Bethe ansatz. The Bethe equations show that fractional statistics effectively account for coupling an external gauge field to an integer statistics' system.

arXiv:cond-mat/9803074•Physical review. B, Condensed matter•Jul 15, 1998•44 citations

Exact Solution of a New Class of Hubbard-Type Models with Open Boundary Conditions

Cao Li

A new class of Hubbard-type models with open boundary conditions in one dimension is studied in the frame- work of coordinate Bethe ansatz method.The energy spectrum,integrable boundary conditions and the corresponding Bethe ansatz equations are derived.

Chinese Physics C•Jan 1, 2007•0 citations

Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields

Yuanyuan Li, Junpeng Cao, Wen‐Li Yang +2 more

The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector is constructed. It is shown that the second eigenvalue problem can be transformed into that of the inhomogeneous XXX spin chain with arbitrary boundary fields which can be solved via the off-diagonal Bethe ansatz method.

arXiv:1311.0432•Nuclear Physics B•Dec 11, 2013•36 citations

The Bethe ansatz solution

Fabian H. L. Eßler, Holger Frahm, Frank Göhmann +2 more

The bare existence of this book is due to the amazing fact that the solution of the stationary Schrödinger equation for the one-dimensional Hubbard model can be reduced to a set of algebraic equations, which is tractable in the thermodynamic limit. These equations will be derived in this chapter. We will call them the Lieb-Wu equations to honour E. H. Lieb and F. Y. Wu, who first obtained them [298]. The derivation is based on a method, called the nested (coordinate) Bethe ansatz, which goes back to the seminal articles of C. N. Yang [493] and M. Gaudin [154], who generalized earlier work [60, 296] on exactly solvable models to models with internal degrees of freedom. The roots of the Lieb-Wu equations parameterize the eigenvalues and the eigenstates of the Hamiltonian of the one-dimensional Hubbard model. They encode the complete information about the model. These roots are not explicitly known in the general N -particle case. In the thermodynamic limit ( N →∞), however, only the distributions of the roots in the complex plane matter, and many physical quantities can be calculated as solutions of linear or non-linear Fredholm type integral equations. Moreover, it is sometimes possible to use the Lieb-Wu equations in an implicit way even for finite N , e.g., in the proof of the SO(4) highest weight properties of the eigenstates in Sections 3.D and 3.F of the appendix or in the calculation of their norm in Section 3.5.

Cambridge University Press eBooks•Feb 7, 2005•1 citation
We define one-dimensional particles with generalized exchange statistics. The exact solution of a Hubbard-type Hamiltonian constructed with such particles is achieved using the coordinate Bethe Ansatz. The chosen deformation of the statistics is equivalent to the presence of a magnetic field produced by the particles themselves, which is also present in a `free gas' of these particles.
We define one-dimensional particles as non-Abelian representations of the symmetric group SN.{S}_{N}.SN​. The exact solution of an XXZ\mathrm{XXZ}XXZ type Hamiltonian built up with such particles is achieved using the coordinate Bethe ansatz. The Bethe equations show that fractional statistics effectively account for coupling an external gauge field to an integer statistics' system.
The bare existence of this book is due to the amazing fact that the solution of the stationary Schrödinger equation for the one-dimensional Hubbard model can be reduced to a set of algebraic equations, which is tractable in the thermodynamic limit. These equations will be derived in this chapter. We will call them the Lieb-Wu equations to honour E. H. Lieb and F. Y. Wu, who first obtained them [298]. The derivation is based on a method, called the nested (coordinate) Bethe ansatz, which goes back to the seminal articles of C. N. Yang [493] and M. Gaudin [154], who generalized earlier work [60, 296] on exactly solvable models to models with internal degrees of freedom. The roots of the Lieb-Wu equations parameterize the eigenvalues and the eigenstates of the Hamiltonian of the one-dimensional Hubbard model. They encode the complete information about the model. These roots are not explicitly known in the general N -particle case. In the thermodynamic limit ( N →∞), however, only the distributions of the roots in the complex plane matter, and many physical quantities can be calculated as solutions of linear or non-linear Fredholm type integral equations. Moreover, it is sometimes possible to use the Lieb-Wu equations in an implicit way even for finite N , e.g., in the proof of the SO(4) highest weight properties of the eigenstates in Sections 3.D and 3.F of the appendix or in the calculation of their norm in Section 3.5.