Bosonization solution of the Falicov-Kimball model

TL;DR

This paper introduces a bosonization approach to analyze the one-dimensional spinless Falicov-Kimball model, revealing the origin of ordering, crossover behavior, and electronic polarons, with a detailed phase diagram.

Contribution

It presents a novel bosonization method for the Falicov-Kimball model and extends analysis to include hybridization effects and intermediate coupling phenomena.

Findings

Effective model clarifies the origin of ordering.

Identifies a crossover between weak and strong coupling.

Confirms the existence of electronic polarons at intermediate coupling.

Abstract

We use a novel approach to analyze the one dimensional spinless Falicov-Kimball model. We derive a simple effective model for the occupation of the localized orbitals which clearly reveals the origin of the known ordering. Our study is extended to a quantum model with hybridization between the localized and itinerant states; we find a crossover between the well-known weak- and strong-coupling behaviour. The existence of electronic polarons at intermediate coupling is confirmed. A phase diagram is presented and discussed in detail.