Recently an exact SU(2)⊗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.

• Received 18 March 1992

DOI:https://doi.org/10.1103/PhysRevLett.69.1695