Abstract
This work present a new class of variational wave functions for fermi systems in any dimension. These wave functions introduce correlations between Cooper pairs in different momentum states and the relevant correlations can be computed analytically. At half filling we have a ground state with critical superconducting correlations, that is argued to be exact for the model considered. We find large enhancements in a Cooper pair correlation function caused purely by the interplay between the uncertainty principle, repulsion and the proximity of half filling. This is surprising since there is no accompanying signature in usual charge and spin response functions, and typifies a novel kind of many body cooperative behaviour.
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