Static and dynamic properties of the spinless Falicov-Kimball model

Abstract

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 ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}}_{k}$, 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 ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}}_{k}$ 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 $U$.