  In this paper, we discuss physical consequences of pseudospin SU(2) symmetry
breaking in the negative-U Hubbard model at half-filling. If pseudospin
symmetry is spontaneously broken while its unique subgroup U(1) remains
invariant, it will lead to the charge density wave (CDW) ground state.
Furthermore, if the U(1) symmetry is also broken, the ground state will have
the off-diagonal long range order (ODLRO), signaling a superconductor. In this
case, CDW and superconductivity coexist to form a supersolid. Finally, we show
that CDW suppresses, but does not destroy superconductivity.
