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

Solid State Communications

Spin analog method for collective modes of the Hubbard model

E. J. Melé

Published Aug 1, 1991• 0 citations
Publisher

Abstract

We make use of a canonical transformation relating the positive U and negative U sectors of the one band Hubbard model to study the global SU(2) pseudospin symmetry in the model, and to investigate the structure of the collective excitation spectrum from a superconducting ground state in the model. New collective modes in this model associated with the SU(2) pseudospin symmetry, recently discussed by Zhang, appear in the pseudo-spinwave spectrum of the transformed problem. Consequences of this mapping for a self dual generalization of the Hubbard model are also discussed.

DOI
10.1016/0038-1098(91)90042-t

Related papers

SO(4) Symmetry of the Hubbard Model and its Experimental Consequences

Shoucheng Zhang

The one band Hubbard model on a bi-partite lattice possess a global SO(4) symmetry group which is a direct product of the spin SU(2) and the pseudospin SU(2) symmetry group. Recently, the group theorectical consequence of this symmetry property has been investigated systematically. It is shown that this symmetry property can be used to reduce the complexity of diagonalizing the Hubbard Hamiltonian, and classify all the eigenstates according to the representation of the SO(4) group. It also leads to an exact one-to-one corespondence of the eigenstates at half-filling to that away from half-filling. Most importantly however, it is shown that this symmetry property leads to a direct experimental prediction for the high Tc superconductivity. If the high Tc superconductivity is correctly described by the Hubbard model, then the SO(4) symmetry dictates the existence of a collective mode that only appears below the superconducting transition temperature. Such a mode can be detected in an electron energy loss experiment as a sharp resonance feature. The location of the peak measure the parameters in the Hubbard model, the intensity is proportional to the superconducting order parameter and the width measures the departure of the Hubbard model from reality.

International Journal of Modern Physics B•Jan 1, 1991•28 citations

Pseudospin symmetry and new collective modes of the Hubbard model

Shoucheng Zhang

The Hubbard model possesses a SU(2) pseudospin symmetry, which contains the U(1) phase symmetry as a subgroup. The existence of such symmetry leads to interesting experimental consequences if the U(1) phase symmetry is spontaneously broken, i.e., if the ground state is superconducting. In this case, there must exist a pair of massive collective modes which together with the usual Goldstone mode form a triplet representation of the psuedospin group. These collective modes are collisionless and couple directly to external charge disturbances with wave number \ensuremath{\pi} and can therefore be detected experimentally as sharp resonances.

Physical Review Letters•Jul 2, 1990•189 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

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

Ward-Takahashi relations for SO(4) symmetry in the Hubbard model

Atsushi Masumizu, Kiyoshi Sogo

Ward-Takahashi relations for spin symmetry $\mathrm{SU}{(2)}_{\mathrm{S}}$ and pseudospin symmetry $\mathrm{SU}{(2)}_{\mathrm{C}}$ are derived for the simple Hubbard model in arbitrary dimensions. For this purpose we generally discuss local SO(4) symmetry in terms of Clifford algebra, and employ a gauge transformed form of the original Hubbard Hamiltonian, which makes the Ward-Takahashi relations much simpler. Derived Ward-Takahashi relations are rewritten as the relations between self-energy and vertex part to discuss spontaneously broken symmetry and Fermi liquid property of the system for zero temperature magnetism.

Physical Review B•Sep 12, 2005•7 citations

Comment on ‘‘Pseudospin symmetry and new collective modes of the Hubbard model’’

I. A. Fomin, Peter Schmitteckert, P. Wölfle

A Comment on the Letter by Shoucheng Zhang Phys. Rev. Lett. 65, 120 (1990).Received 7 November 1991DOI:https://doi.org/10.1103/PhysRevLett.69.214©1992 American Physical Society

Physical Review Letters•Jul 6, 1992•7 citations
We make use of a canonical transformation relating the positive U and negative U sectors of the one band Hubbard model to study the global SU(2) pseudospin symmetry in the model, and to investigate the structure of the collective excitation spectrum from a superconducting ground state in the model. New collective modes in this model associated with the SU(2) pseudospin symmetry, recently discussed by Zhang, appear in the pseudo-spinwave spectrum of the transformed problem. Consequences of this mapping for a self dual generalization of the Hubbard model are also discussed.
The one band Hubbard model on a bi-partite lattice possess a global SO(4) symmetry group which is a direct product of the spin SU(2) and the pseudospin SU(2) symmetry group. Recently, the group theorectical consequence of this symmetry property has been investigated systematically. It is shown that this symmetry property can be used to reduce the complexity of diagonalizing the Hubbard Hamiltonian, and classify all the eigenstates according to the representation of the SO(4) group. It also leads to an exact one-to-one corespondence of the eigenstates at half-filling to that away from half-filling. Most importantly however, it is shown that this symmetry property leads to a direct experimental prediction for the high Tc superconductivity. If the high Tc superconductivity is correctly described by the Hubbard model, then the SO(4) symmetry dictates the existence of a collective mode that only appears below the superconducting transition temperature. Such a mode can be detected in an electron energy loss experiment as a sharp resonance feature. The location of the peak measure the parameters in the Hubbard model, the intensity is proportional to the superconducting order parameter and the width measures the departure of the Hubbard model from reality.
The Hubbard model possesses a SU(2) pseudospin symmetry, which contains the U(1) phase symmetry as a subgroup. The existence of such symmetry leads to interesting experimental consequences if the U(1) phase symmetry is spontaneously broken, i.e., if the ground state is superconducting. In this case, there must exist a pair of massive collective modes which together with the usual Goldstone mode form a triplet representation of the psuedospin group. These collective modes are collisionless and couple directly to external charge disturbances with wave number \ensuremath{\pi} and can therefore be detected experimentally as sharp resonances.
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.
Ward-Takahashi relations for spin symmetry SU(2)S\mathrm{SU}{(2)}_{\mathrm{S}}SU(2)S​ and pseudospin symmetry SU(2)C\mathrm{SU}{(2)}_{\mathrm{C}}SU(2)C​ are derived for the simple Hubbard model in arbitrary dimensions. For this purpose we generally discuss local SO(4) symmetry in terms of Clifford algebra, and employ a gauge transformed form of the original Hubbard Hamiltonian, which makes the Ward-Takahashi relations much simpler. Derived Ward-Takahashi relations are rewritten as the relations between self-energy and vertex part to discuss spontaneously broken symmetry and Fermi liquid property of the system for zero temperature magnetism.