SO 4 SYMMETRY IN A HUBBARD MODEL

Chen Ning Yang, S.-C. Zhang

Chen Ning Yang, S.-C. Zhang

Chen Ning Yang, Shoucheng Zhang

For a simple Hubbard model, using a particle-particle pairing operator η and a particle-hole pairing operator ζ, it is shown that one can write down two commuting sets of angular momenta operators J and J′, both of which commute with the Hamiltonian. These considerations allow the introduction of quantum numbers j and j′, and lead to the fact that the system has SO 4 = ( SU 2 × SU 2)/ Z 2 symmetry. j is related to the existence of superconductivity for a state and j′ to its magnetic properties.

Chen Ning Yang

Harald Grosse

Roberto Livi, Arianna Montorsi, Mario Rasetti

The effects of different linearization procedures as breaking of the global symmetry of the Hubbard model recently discovered by Yang and Zhang are discussed, together with the ensuing order parameters. In particular it is pointed out how only the Fermi linearization technique allows us both to restore the complete symmetry in the disordered phase, and to describe an ordered phase characterized by an order parameter associated with the breaking of the superconductive symmetry.