Static and dynamic properties of the spinless Falicov-Kimball model

The spinless Falicov-Kimball model is studied by the use of a recently developed projector-based renormalization method for many-particle Hamiltonians. The method is used to evaluate static and dynamic quantities of the one-dimensional model at half-filling. These include the quasiparticle excitation energy epsilon(k), the momentum distribution n(k) of the conduction electrons, and the spatial correlation functions of the localized electrons. One of the most remarkable results is the appearance of a gap in epsilon(k) at the Fermi level of the order of the Coulomb repulsion U, which is accompanied by a smooth behavior for n(k). The density of states for the conduction electrons and the one-particle spectral functions for the localized electrons are also discussed. In both quantities, a gap opens with increasing U.