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/9611014 · Journal of Physics A Mathematical and General

Twisted quantum affine superalgebra , invariantR-matrices and a new integrable electronic model

M. D. Gould, Jon Links, Yao-Zhong Zhang, I. Tsohantjis

Published Jun 21, 1997• 29 citations
arXivHTMLPDF

Abstract

We describe the twisted affine superalgebra and its quantized version . We investigate the tensor product representation of the four-dimensional grade star representation for the fixed-point subsuperalgebra . We work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible. Associated with this four-dimensional grade star representation we derive two invariant R-matrices: one of them corresponds to and the other to . Using the R-matrix for , we construct a new invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly this model reduces in the q = 1 limit, to the one proposed by Essler et al which has a larger symmetry.

DOI
10.1088/0305-4470/30/12/018

Related papers

New R-matrices with non-additive spectral parameters and integrable models of strongly correlated fermions

Yao-Zhong Zhang, Jason L. Werry

Abstract We present a general formula for constructing R-matrices with non-additive spectral parameters associated with a type-I quantum superalgebra. The spectral parameters originate from two one-parameter families of inequivalent finite-dimensional irreducible representations of the quantum superalgebra upon which the R-matrix acts. Applying to the quantum superalgebra Uq(gl(2|1)), we obtain the explicit expression for the Uq(gl(2|1))− invariant R-matrix which is of non-difference form in spectral parameters. Using this R­ matrix we derive a new two-parameter integrable model of strongly correlated electrons with pure imaginary pair hopping terms.

arXiv:2001.05096•Journal of High Energy Physics•Mar 1, 2020•4 citations

A quantum affine algebra for the deformed Hubbard chain

Niklas Beisert, W. Galléas, Takuya Matsumoto

The integrable structure of the one-dimensional Hubbard model is based on Shastry's R -matrix and the Yangian of a centrally extended superalgebra. Alcaraz and Bariev have shown that the model admits an integrable deformation whose R -matrix has recently been found. This R -matrix is of trigonometric type and here we derive its underlying exceptional quantum affine algebra. We also show how the algebra reduces to the above-mentioned Yangian and to the conventional quantum affine algebra in two special limits.

arXiv:1102.5700•Journal of Physics A Mathematical and Theoretical•Aug 22, 2012•44 citations

Finite-temperature correlations for theUq(𝔰𝔩(2|1))-invariant generalized Hubbard model

Kazumitsu Sakai, Andreas Klümper

We study an integrable model of one-dimensional strongly correlated electrons at finite temperature by explicit calculation of the correlation lengths of various correlation functions. The model is invariant with respect to the quantum superalgebra U q ( (2|1)) and characterized by the Hubbard interaction, correlated hopping and pair-hopping terms. Using the integrability, the graded quantum transfer matrix is constructed. From the analyticity of its eigenvalues, a closed set of nonlinear integral equations is derived which describe the thermodynamical quantities and the finite-temperature correlations. The results show a crossover from a regime with dominating density-density correlations to a regime with dominating superconducting pair correlations. Analytical calculations in the low-temperature limit are also discussed.

arXiv:cond-mat/0105416•Journal of Physics A Mathematical and General•Sep 21, 2001•7 citations

INTEGRABLE SYSTEMS ON OPEN CHAINS WITH QUANTUM SUPERSYMMETRY

Jon Links, M. D. Gould

It is demonstrated how one may derive quantum supersymmetric integrable models on an open chain corresponding to (affinizable) irreducible representations of a quantum superalgebra. A new procedure for constructing the transfer matrix is obtained and an expression for the Hamiltonian is given. Applications to Uq(gl(m|n)) invariant systems are discussed in detail. As examples, the q-analogues of several known integrable correlated electron models are presented.

International Journal of Modern Physics B•Nov 15, 1996•17 citations

New Supersymmetric and Exactly Solvable Model of Correlated Electrons

Anthony J. Bracken, M. D. Gould, Jon Links +1 more

A new lattice model is presented for correlated electrons on the unrestricted ${4}^{L}$-dimensional electronic Hilbert space ${\ensuremath{\bigotimes}}_{n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1}^{L}{\mathbf{C}}^{4}$ (where $L$ is the lattice length). It is a supersymmetric generalization of the Hubbard model, but differs from the extended Hubbard model proposed by Essler, Korepin, and Schoutens. The supersymmetry algebra of the new model is superalgebra gl(2 $|$1). The model contains one symmetry-preserving free real parameter which is the Hubbard interaction parameter $U$, and has its origin here in the one-parameter family of inequivalent typical 4-dimensional irreducible representations of gl(2 $|$1). On a one-dimensional lattice, the model is exactly solvable by the Bethe ansatz.

arXiv:cond-mat/9410026•Physical Review Letters•Apr 3, 1995•145 citations

Drinfel'd Twists and Algebraic Bethe Ansatz

Jean Michel Maillet, J.M. Sánchez de Santos

We study representation theory of Drinfel'd twists, in terms of what we call F matrices, associated to finite dimensional irreducible modules of quantum affine algebras, and which factorize the corresponding (unitary) R matrices. We construct explicitly such factorizing F matrices for irreducible tensor products of the fundamental representations of the quantum affine algebra sl2 and its associated Yangian. We then apply these constructions to the XXX and XXZ quantum spins chains of finite length in the framework of the Algebraic Bethe Ansatz.

arXiv:q-alg/9612012•Dec 10, 1996•2 citations
We describe the twisted affine superalgebra and its quantized version . We investigate the tensor product representation of the four-dimensional grade star representation for the fixed-point subsuperalgebra . We work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible. Associated with this four-dimensional grade star representation we derive two invariant R-matrices: one of them corresponds to and the other to . Using the R-matrix for , we construct a new invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly this model reduces in the q = 1 limit, to the one proposed by Essler et al which has a larger symmetry.
Abstract We present a general formula for constructing R-matrices with non-additive spectral parameters associated with a type-I quantum superalgebra. The spectral parameters originate from two one-parameter families of inequivalent finite-dimensional irreducible representations of the quantum superalgebra upon which the R-matrix acts. Applying to the quantum superalgebra Uq(gl(2|1)), we obtain the explicit expression for the Uq(gl(2|1))− invariant R-matrix which is of non-difference form in spectral parameters. Using this R­ matrix we derive a new two-parameter integrable model of strongly correlated electrons with pure imaginary pair hopping terms.
The integrable structure of the one-dimensional Hubbard model is based on Shastry's R -matrix and the Yangian of a centrally extended superalgebra. Alcaraz and Bariev have shown that the model admits an integrable deformation whose R -matrix has recently been found. This R -matrix is of trigonometric type and here we derive its underlying exceptional quantum affine algebra. We also show how the algebra reduces to the above-mentioned Yangian and to the conventional quantum affine algebra in two special limits.
We study an integrable model of one-dimensional strongly correlated electrons at finite temperature by explicit calculation of the correlation lengths of various correlation functions. The model is invariant with respect to the quantum superalgebra U q ( (2|1)) and characterized by the Hubbard interaction, correlated hopping and pair-hopping terms. Using the integrability, the graded quantum transfer matrix is constructed. From the analyticity of its eigenvalues, a closed set of nonlinear integral equations is derived which describe the thermodynamical quantities and the finite-temperature correlations. The results show a crossover from a regime with dominating density-density correlations to a regime with dominating superconducting pair correlations. Analytical calculations in the low-temperature limit are also discussed.
A new lattice model is presented for correlated electrons on the unrestricted 4L{4}^{L}4L-dimensional electronic Hilbert space ${\ensuremath{\bigotimes}}_{n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1}^{L}{\mathbf{C}}^{4}$ (where LLL is the lattice length). It is a supersymmetric generalization of the Hubbard model, but differs from the extended Hubbard model proposed by Essler, Korepin, and Schoutens. The supersymmetry algebra of the new model is superalgebra gl(2 $|$1). The model contains one symmetry-preserving free real parameter which is the Hubbard interaction parameter UUU, and has its origin here in the one-parameter family of inequivalent typical 4-dimensional irreducible representations of gl(2 $|$1). On a one-dimensional lattice, the model is exactly solvable by the Bethe ansatz.
We study representation theory of Drinfel'd twists, in terms of what we call F matrices, associated to finite dimensional irreducible modules of quantum affine algebras, and which factorize the corresponding (unitary) R matrices. We construct explicitly such factorizing F matrices for irreducible tensor products of the fundamental representations of the quantum affine algebra sl2 and its associated Yangian. We then apply these constructions to the XXX and XXZ quantum spins chains of finite length in the framework of the Algebraic Bethe Ansatz.