Static and dynamic properties of the spinless Falicov-Kimball model

TL;DR

This paper investigates the static and dynamic properties of the one-dimensional spinless Falicov-Kimball model at half-filling using a projector-based renormalization method, revealing a Coulomb-repulsion-induced gap in quasiparticle energies.

Contribution

It applies a novel projector-based renormalization method to analyze static and dynamic quantities of the model, providing new insights into gap formation and electron correlations.

Findings

A gap appears in quasiparticle excitation energy at the Fermi level with increasing U.

The momentum distribution remains smooth despite the gap in excitation energies.

Both the density of states and spectral functions develop a gap as U increases.

Abstract

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 $U$.