DEGENERACY OF THE GROUND-STATES AT HALF-FILLING AND THE EXISTENCE OF THE ETA-PAIRING OFF-DIAGONAL LONG-RANGE ORDER IN THE NEGATIVE-U HUBBARD MODELS

Since C.N. Yang proposed the concept of the eta-pairing off-diagonal long-range order (ODLRO), its existence in the negative-U Hubbard models has been discussed by many authors. Recently, Shen and Qiu showed explicitly that the eta-pairing ODLRO exists in some ground states of the negative-U Hubbard models defined on a certain type of bipartite lattices. In this article, we shall show that these states are, in fact, the only ground states which have eta-pairing ODLRO. Finally, we shall briefly discuss the experimental implication of our results.