  We study the underlying symmetry in a spin-orbit coupled tight-binding model
with Hubbard interaction. It is shown that, in the absence of the on-site
interaction, the system possesses the SU(2) symmetry arising from the
timereversal symmetry. The influence of the on-site interaction on the symmetry
depends on the topology of the networks: The SU(2) symmetry is shown to be the
spin rotation symmetry of a simply-connected lattice, so it still holds in the
presence of the Hubbard correlation. In contrary, the on-site interaction
breaks the SU(2) symmetry of a multi-connected lattice.
