So4 Symmetry in a Hubbard Model

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.