Abstract
Using Bogoliubov's inequality we rigorously show that the one- and two-dimensional Hubbard model with narrow bands does not exhibit long-range order for different kinds of pairing, e.g. s-wave Cooper pairing and generalized η pairing. This result holds at any finite temperature for both repulsive and attractive Coulomb interactions. At zero temperature there will be no on-site electron pairing long-range order if a gap in the charge excitation spectrum exists. The present results do not cover the case of d x 2− y 2 pairing of electrons.
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