The action of the nearest neighbor Coulomb repulsion on the homogeneity in the high concentration domain for itinerant systems

Exact results are presented for itinerant systems demonstrating that the nearest neighbor Coulomb repulsion (V) destroys the homogeneity in the high concentration regime, this property being not present in the low concentration domain. Since the effects of V often seem contradictory, and the number of phases in which it could appear is extremely large, this result underlines that the action of the nearest neighbor repulsion is not necessarily routed in the characteristics of phases on which it acts, but could be intimately related to V itself. The [Formula: see text] case usually means nonintegrability, hence the deduced exact ground states are related to nonintegrable systems, the technique being based on positive semidefinite operator properties.