Abstract
Since Yang [Phys. Rev. Lett 63 (1989) 2144] proposed the possible existence of the η-pairing off-diagonal long-range order (ODLRO) in the ground states of the negative- U Hubbard model, this problem has been studied by many physicists. In this article, based on our previous work, we shall rigorously show that all the ground states, which have the η-pairing ODLRO, are actually supersolid rather than superfluid as one expected before.
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