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 (PRM) for many-particle Hamiltonians. The method is used to evaluate static and dynamic quantities of the one-dimensional model at half-filling. To these belong the quasiparticle excitation energy $\tilde{\epsilon}_k$ and the momentum distribution $n_k$ of the conduction electrons and spatial correlation functions of the localized electrons. One of the most remarkable results is the appearance of a gap in $\tilde{\epsilon}_k$ 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 $U$.