Abstract
We show that in the translation invariant case and in the antiferromagnetic phase the reduced density matrix ϱ 2 has no off-diagonal long-range order of on-site electron pairs for the single-band Hubbard model on a cubic lattice away from half filling at finite temperatures both for the positive coupling and for the negative coupling. In these cases the model cannot give a mechanism for the superconductivity caused by the condensation of on-site electron pairs and the nearest-neighbor electron pairs.
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