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/9701111

Hubbard Models with Superconducting Quantum Symmetry

Peter Schupp

Published Jan 16, 1997• 0 citations
arXivHTMLPDF

Abstract

We discuss classical and quantum symmetries of extended Hubbard models. The quantum symmetries are shown to be related to the known superconducting SU(2) symmetry of the original Hubbard model at half filling via generalized Lang-Firsov transformations and Drinfel'd twists. (Based on talk at the 21st ICGTM in Goslar, July 1996)
DOI
10.48550/arxiv.cond-mat/9701111

Related papers

Symmetries and canonical transformations of the Hubbard model on bipartite lattices

Stellan OIUMLstlund

Recently an exact SU(2)\ensuremath{\bigotimes}SU(2) symmetry for the half-filled Hubbard model has been elucidated but has not yet been properly incorporated in many analyses of this model. We compute the irreducible representations of the symmetry group, a necessary step for any consistent mean-field analysis. A proper mean-field theory valid for both negative- and positive-U Hubbard models is then presented. A by-product of the description is a systematic enumeration of the Lie group SU(8) of unitary canonical transformations that is a direct generalization of the SU(4) transformation in the theory of superfluid $^{3}\mathrm{He}$ and the SU(2) Bogoliubov transformation in BCS theory.

Physical Review Letters•Sep 14, 1992•20 citations

Pseudo-spin symmetry in the Hubbard model

J. P. Wallington, James F. Annett

We present a hidden SU(2) ‘pseudo-spin’ symmetry of the half-filled Hubbard model, relating superconducting and charge orderings. Using an appropriate functional integral representation, we show the consequences of this symmetry for the quasiparticle excitation spectrum.

Philosophical Magazine B•Nov 1, 1997•3 citations

Quantum symmetries induced by phonons in the Hubbard model

Arianna Montorsi, Mario Rasetti

We show how the addition of a phonon field to the Hubbard model deforms the superconducting su(2) part of the global symmetry Lie algebra su(2)\ensuremath{\bigotimes}su(2)/${\mathit{openZ}}_{2}$, holding at half filling for the customary model, into a quantum [su(2)${]}_{\mathit{q}}$ symmetry, holding for a filling which depends on the electron-phonon interaction strength. Such symmetry originates in the feature that in the presence of phonons the hopping amplitude turns out to depend on the coupling strength. The states generated by resorting to this q symmetry exhibit both off-diagonal long-range order and pairing.

Physical Review Letters•Mar 14, 1994•13 citations

On the SU(2)×SU(2) symmetry in the Hubbard model

Dorota Jakubczyk, Paweł Jakubczyk

Abstract We discuss the one-dimensional Hubbard model, on finite sites spin chain, in context of the action of the direct product of two unitary groups SU(2)×SU(2). The symmetry revealed by this group is applicable in the procedure of exact diagonalization of the Hubbard Hamiltonian. This result combined with the translational symmetry, given as the basis of wavelets of the appropriate Fourier transforms, provides, besides the energy, additional conserved quantities, which are presented in the case of a half-filled, four sites spin chain. Since we are dealing with four elementary excitations, two quasiparticles called “spinons”, which carry spin, and two other called “holon” and “antyholon”, which carry charge, the usual spin-SU(2) algebra for spinons and the so called pseudospin-SU(2) algebra for holons and antiholons, provide four additional quantum numbers.

Open Physics•May 30, 2012•7 citations

GLOBAL AND GAUGE SYMMETRIES OF THE HUBBARD MODEL

Elisa Ercolessi, G. Morandi, F. Ortolani

A remarkable global SO(4) symmetry of the Hubbard model, when there is on the average one electron per site (“weak” half-filling condition) has been recently uncovered by Yang and Zhang. We discuss here its relationship to the SU(2) gauge symmetry of the model that holds when there is exactly one electron per site (“strong” half-filling condition) as well as its possible generalizations to lattice structures more general than those considered by Yang and Zhang.

Modern Physics Letters B•Jan 20, 1992•2 citations

Symmetries and mean-field phases of the extended Hubbard model

Anders B. Eriksson, Torbjörn Einarsson, Stellan S. Ostlund

The two-dimensional extended Hubbard model that includes a nearest-neighbor Heisenberg interaction is studied using a mean-field theory where quasiparticles are defined by an U(8) group of canonical transformations permitting both broken gauge, spin, and sublattice symmetry. The theory is further extended to incorporate a possible twist in the spin-quantization axis, so that the competition between superconductivity, charge density waves, and N\'eel and spiral antiferromagnetic order can be monitored within one single theory. Our results for positive Hubbard U and Heisenberg exchange J suggest that antiferromagnetic ordering dominates close to half-filling, while spiral states and d-wave superconductivity compete when doping is introduced. For moderate values of J, we find a phase diagram where a phase transition occurs from an antiferromagnet to a d-wave superconductor as doping is increased. A narrow region of (s+id)-wave superconductor is found for some values of J and U.

arXiv:cond-mat/9411071•Physical review. B, Condensed matter•Aug 1, 1995•20 citations
Recently an exact SU(2)\ensuremath{\bigotimes}SU(2) symmetry for the half-filled Hubbard model has been elucidated but has not yet been properly incorporated in many analyses of this model. We compute the irreducible representations of the symmetry group, a necessary step for any consistent mean-field analysis. A proper mean-field theory valid for both negative- and positive-U Hubbard models is then presented. A by-product of the description is a systematic enumeration of the Lie group SU(8) of unitary canonical transformations that is a direct generalization of the SU(4) transformation in the theory of superfluid 3He^{3}\mathrm{He}3He and the SU(2) Bogoliubov transformation in BCS theory.
We show how the addition of a phonon field to the Hubbard model deforms the superconducting su(2) part of the global symmetry Lie algebra su(2)\ensuremath{\bigotimes}su(2)/openZ2{\mathit{openZ}}_{2}openZ2​, holding at half filling for the customary model, into a quantum [su(2)]q{]}_{\mathit{q}}]q​ symmetry, holding for a filling which depends on the electron-phonon interaction strength. Such symmetry originates in the feature that in the presence of phonons the hopping amplitude turns out to depend on the coupling strength. The states generated by resorting to this q symmetry exhibit both off-diagonal long-range order and pairing.
Abstract We discuss the one-dimensional Hubbard model, on finite sites spin chain, in context of the action of the direct product of two unitary groups SU(2)×SU(2). The symmetry revealed by this group is applicable in the procedure of exact diagonalization of the Hubbard Hamiltonian. This result combined with the translational symmetry, given as the basis of wavelets of the appropriate Fourier transforms, provides, besides the energy, additional conserved quantities, which are presented in the case of a half-filled, four sites spin chain. Since we are dealing with four elementary excitations, two quasiparticles called “spinons”, which carry spin, and two other called “holon” and “antyholon”, which carry charge, the usual spin-SU(2) algebra for spinons and the so called pseudospin-SU(2) algebra for holons and antiholons, provide four additional quantum numbers.
The two-dimensional extended Hubbard model that includes a nearest-neighbor Heisenberg interaction is studied using a mean-field theory where quasiparticles are defined by an U(8) group of canonical transformations permitting both broken gauge, spin, and sublattice symmetry. The theory is further extended to incorporate a possible twist in the spin-quantization axis, so that the competition between superconductivity, charge density waves, and N\'eel and spiral antiferromagnetic order can be monitored within one single theory. Our results for positive Hubbard U and Heisenberg exchange J suggest that antiferromagnetic ordering dominates close to half-filling, while spiral states and d-wave superconductivity compete when doping is introduced. For moderate values of J, we find a phase diagram where a phase transition occurs from an antiferromagnet to a d-wave superconductor as doping is increased. A narrow region of (s+id)-wave superconductor is found for some values of J and U.