Constraints on s-wave pairing in the Hubbard model

We present an exact identity between the on-site and the extended s-wave pairing amplitudes in the Hubbard model. We prove that the extended s-wave pairing amplitude vanishes identically at half filling for both signs of U. Away from half filling, the existence of an on-site s-wave pairing is a necessary and sufficient condition for the existence of an extended s-wave pairing. This result gives rise to constraints on the possible symmetries of the superconducting gap in the Hubbard model. © 1990 The American Physical Society.