PERIODIC GROUND-STATES IN SIMPLE-MODELS OF ITINERANT FERMIONS INTERACTING WITH CLASSICAL FIELDS

A model of itinerant lattice electrons interacting with classical nucl ei is studied. The electrons can interact between themselves via a Hub bard on-site term. It is shown that, in the ground state of the half-f illed band, the nuclei form a periodic crystal. More precisely for a c ubic lattice they form a chessboard state under some appropriate condi tion on the hopping matrix. This generalizes known results previously obtained for the Falicov-Kimball model. The case where fermions are re placed by hard-core bosons in this later model is also discussed. More generally models of fermions interacting with classical scalar or vec tor fields are briefly considered. The mathematical technique used is ''reflection positivity'' adapted to the case of Fermi statistics.