Ground state properties of the spinless Falicov-Kimball model: Crystallization and metal-insulator transitions off the hole-particle symmetry point

Properties of grounds states of an itinerant electron model (which can be regarded as the one-band, spinless Falicov-Kimball model) beyond the hole-particle symmetry point are studied. The underlying lattice is chosen to be a square lattice. Using exact and numerical arguments it is shown that when the density of band electrons is varied different sorts of periodic configurations of localized particles (f-electrons) minimize the energy. The one- particle densities of states of the band electrons corresponding to these configurations are presented. The system can be a metal or an insulator accordingly. Moreover, for some densities of band electrons a metal-insulator transition, driven by the unique parameter of the system, takes place. The importance of many-body effects is revealed.