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/9707275 · Physical Review Letters

Exact Realization of SO(5) Symmetry in Extended Hubbard Models

Christopher L. Henley

Published Apr 20, 1998• 46 citations
arXivHTMLPDF

Abstract

Zhang recently conjectured an approximate SO(5) symmetry relating antiferromagnetic and superconducting states in high- ${T}_{c}$ cuprates. Here, an exact SO(5) symmetry is implemented in a generalized Hubbard model (with long-range interactions) on a lattice. The possible relation to a more realistic extended Hubbard Hamiltonian is discussed.

DOI
10.1103/physrevlett.80.3590

Related papers

From Antiferromagnetism to Superconductivity: Numerical Evidence for SO(5) Symmetry

R. Eder, Werner R. Hanke, S. C. Zhang

In this work, we present numerical results which support SO(5) symmetry as a concept unifying superconductivity and antiferromagnetism in the high-temperature superconductors. Using exact cluster diagonalization, we verify the recently proposed SO(5) multiplet structures for a widely used microscopic model, the t-J model. Our results show that the d-wave superconducting ground states away from half-filling are obtained from the higher spin states at half-filling through SO(5) rotations, that the dominant low energy resonance in the dynamical spin correlation function corresponds to a `pi-resonance' in the entire low doping region, and that the SO(5) symmetry is robust against inclusion of longer ranged Coulomb repulsion and next-nearest neighbor hopping.

arXiv:cond-mat/9707233•Jul 22, 1997•0 citations

SO(5) as a critical dynamical symmetry in the SU(4) model of high-temperature superconductivity

Lian-Ao Wu, Mike Guidry, Yang Sun +1 more

An SU(4) model of high-temperature superconductivity and antiferromagnetism has recently been proposed. The SO(5) group employed by Zhang [Science 275, 1089 (1997)] is embedded in this SU(4) as a subgroup, suggesting a connection between our SU(4) model and the Zhang SO(5) model. In order to understand the relationship between the the two models, we have used generalized coherent states to analyze the nature of the SO(5) subgroup. By constructing coherent-state energy surfaces, we demonstrate explicitly that the $\mathrm{SU}(4)\ensuremath{\supset}\mathrm{SO}(5)$ symmetry can be interpreted as a critical dynamical symmetry interpolating between superconducting and antiferromagnetic phases, and that this critical dynamical symmetry has many similarities to critical dynamical symmetries identified previously in other fields of physics. More generally, we demonstrate with this example that the mathematical techniques associated with generalized coherent states may have powerful applications in condensed-matter physics because they provide a clear connection between microscopic many-body theories and their broken-symmetry approximate solutions. In addition, these methods may be interpreted as defining the most general Bogoliubov transformation subject to a Lie group symmetry constraint, thus providing a mathematical connection between algebraic formulations and the language of quasiparticle theory. Finally, we suggest that the identification of the SO(5) symmetry as a critical dynamical symmetry implies deep algebraic connections between high-temperature superconductors and seemingly unrelated phenomena in other field of physics.

arXiv:cond-mat/0208329•Physical review. B, Condensed matter•Jan 17, 2003•24 citations

Numerical evidence for SO(5) symmetry and superspin multiplets in the two-dimensional t−J model

R. Eder, Werner R. Hanke, Shoucheng Zhang

In this work, we present numerical results which support SO(5) symmetry as a concept unifying superconductivity and antiferromagnetism in the high-temperature superconductors. Using exact cluster diagonalization, we verify that low-energy states of the $t\ensuremath{-}J$ model, a widely used microscopic model for the high-${T}_{c}$ cuprates, form SO(5) symmetry multiplets. Our results show that the $d$-wave superconducting ground states away from half-filling are obtained from the higher-spin states at half-filling through SO(5) rotations. The SO(5) symmetry is found to be robust against the inclusion of longer-ranged Coulomb repulsion and next-nearest-neighbor hopping.

Physical review. B, Condensed matter•Jun 1, 1998•26 citations

Boson Realization of the SU(4) Model of High-Temperature Superconductivity

Jan Dobeš

The SU(4) algebraic model of high-temperature superconductivity is studied employing the boson mapping techniques. The bosonization of the model enables us to get exact numerical solution of the model. The order parameters are discussed. The situation close to the SO(5) dynamical symmetry limit is interpreted as a modelling case for the behaviour of $D$-wave superconducting and antiferromagnetic phases in cuprates.

arXiv:cond-mat/9912369•Dec 20, 1999•0 citations

Hubbard model with SU(4) symmetry

Eugene Pivovarov

In the model considered, the nonlocal interaction of the fermions in different sublattices of a bipartite lattice is introduced. It can also be regarded as local interaction of fermions with opposite ``hypercharge''. The corresponding term in the Hamiltonian is SU(4)-invariant and appears to be the most tractable version of the SO(5)-invariant model that unifies antiferromagnetic and d-wave superconducting order parameters. The model has been studied primarily in the weak interaction limit and in the mean field approximation. Near the half-filling the antiferromagnetic critical temperature has a peak. However, the superconducting transition takes place when the Fermi surface crosses the area where the density of states is of order of inverse coupling coefficient. Thus, in mean-field approximation, there exist an interval of values of the chemical potential, for which the system is a superconductor for arbitrary high temperatures. The temperature dependence of specific heat, Hall coefficient, and DC conductivity in the normal phase agrees with that experimentally observed in high-$T_c$ cuprates.

arXiv:cond-mat/9807291•Jul 23, 1998•0 citations

Finite-Size Studies on the SO(5) Symmetry of the Hubbard Model

Stefan Meixner, Werner R. Hanke, Eugene Demler +1 more

We present numerical evidence for the approximate SO(5) symmetry of the Hubbard model on a 10-site cluster. Various dynamic correlation functions involving the $\ensuremath{\pi}$ operators, the generators of the SO(5) algebra, are studied using exact diagonalization, and are found to possess sharp collective peaks. Our numerical results also lend support to the interpretation of the recent resonant neutron scattering peaks in the YBCO superconductors in terms of the Goldstone modes of the spontaneously broken SO(5) symmetry. Perturbations such as longer-ranged hoppings and interactions do not suppress the $\ensuremath{\pi}$ resonance in interesting parameter regimes.

arXiv:cond-mat/9701217•Physical Review Letters•Dec 15, 1997•43 citations
Zhang recently conjectured an approximate SO(5) symmetry relating antiferromagnetic and superconducting states in high- Tc{T}_{c}Tc​ cuprates. Here, an exact SO(5) symmetry is implemented in a generalized Hubbard model (with long-range interactions) on a lattice. The possible relation to a more realistic extended Hubbard Hamiltonian is discussed.
In this work, we present numerical results which support SO(5) symmetry as a concept unifying superconductivity and antiferromagnetism in the high-temperature superconductors. Using exact cluster diagonalization, we verify the recently proposed SO(5) multiplet structures for a widely used microscopic model, the t-J model. Our results show that the d-wave superconducting ground states away from half-filling are obtained from the higher spin states at half-filling through SO(5) rotations, that the dominant low energy resonance in the dynamical spin correlation function corresponds to a `pi-resonance' in the entire low doping region, and that the SO(5) symmetry is robust against inclusion of longer ranged Coulomb repulsion and next-nearest neighbor hopping.
An SU(4) model of high-temperature superconductivity and antiferromagnetism has recently been proposed. The SO(5) group employed by Zhang [Science 275, 1089 (1997)] is embedded in this SU(4) as a subgroup, suggesting a connection between our SU(4) model and the Zhang SO(5) model. In order to understand the relationship between the the two models, we have used generalized coherent states to analyze the nature of the SO(5) subgroup. By constructing coherent-state energy surfaces, we demonstrate explicitly that the $\mathrm{SU}(4)\ensuremath{\supset}\mathrm{SO}(5)$ symmetry can be interpreted as a critical dynamical symmetry interpolating between superconducting and antiferromagnetic phases, and that this critical dynamical symmetry has many similarities to critical dynamical symmetries identified previously in other fields of physics. More generally, we demonstrate with this example that the mathematical techniques associated with generalized coherent states may have powerful applications in condensed-matter physics because they provide a clear connection between microscopic many-body theories and their broken-symmetry approximate solutions. In addition, these methods may be interpreted as defining the most general Bogoliubov transformation subject to a Lie group symmetry constraint, thus providing a mathematical connection between algebraic formulations and the language of quasiparticle theory. Finally, we suggest that the identification of the SO(5) symmetry as a critical dynamical symmetry implies deep algebraic connections between high-temperature superconductors and seemingly unrelated phenomena in other field of physics.
In this work, we present numerical results which support SO(5) symmetry as a concept unifying superconductivity and antiferromagnetism in the high-temperature superconductors. Using exact cluster diagonalization, we verify that low-energy states of the $t\ensuremath{-}J$ model, a widely used microscopic model for the high-Tc{T}_{c}Tc​ cuprates, form SO(5) symmetry multiplets. Our results show that the ddd-wave superconducting ground states away from half-filling are obtained from the higher-spin states at half-filling through SO(5) rotations. The SO(5) symmetry is found to be robust against the inclusion of longer-ranged Coulomb repulsion and next-nearest-neighbor hopping.
The SU(4) algebraic model of high-temperature superconductivity is studied employing the boson mapping techniques. The bosonization of the model enables us to get exact numerical solution of the model. The order parameters are discussed. The situation close to the SO(5) dynamical symmetry limit is interpreted as a modelling case for the behaviour of DDD-wave superconducting and antiferromagnetic phases in cuprates.
In the model considered, the nonlocal interaction of the fermions in different sublattices of a bipartite lattice is introduced. It can also be regarded as local interaction of fermions with opposite ``hypercharge''. The corresponding term in the Hamiltonian is SU(4)-invariant and appears to be the most tractable version of the SO(5)-invariant model that unifies antiferromagnetic and d-wave superconducting order parameters. The model has been studied primarily in the weak interaction limit and in the mean field approximation. Near the half-filling the antiferromagnetic critical temperature has a peak. However, the superconducting transition takes place when the Fermi surface crosses the area where the density of states is of order of inverse coupling coefficient. Thus, in mean-field approximation, there exist an interval of values of the chemical potential, for which the system is a superconductor for arbitrary high temperatures. The temperature dependence of specific heat, Hall coefficient, and DC conductivity in the normal phase agrees with that experimentally observed in high-TcT_cTc​ cuprates.
We present numerical evidence for the approximate SO(5) symmetry of the Hubbard model on a 10-site cluster. Various dynamic correlation functions involving the $\ensuremath{\pi}$ operators, the generators of the SO(5) algebra, are studied using exact diagonalization, and are found to possess sharp collective peaks. Our numerical results also lend support to the interpretation of the recent resonant neutron scattering peaks in the YBCO superconductors in terms of the Goldstone modes of the spontaneously broken SO(5) symmetry. Perturbations such as longer-ranged hoppings and interactions do not suppress the $\ensuremath{\pi}$ resonance in interesting parameter regimes.