Falicov-Kimball Models: A Partial Review of the Ground States Problem

TL;DR

This review explores the complex ground state properties of Falicov-Kimball models across various dimensions, highlighting their rich structures, particle statistics effects, and lattice influences, including discussions on the flux phase problem.

Contribution

It provides a biased overview of the diverse ground state phenomena in Falicov-Kimball models, emphasizing the effects of particle statistics and lattice structure.

Findings

Rich variety of ground states in Falicov-Kimball models

Differences between fermions and hard-core bosons

Impact of lattice bipartiteness on properties

Abstract

In this review we present a biased review of the ground state properties of the Falicov-Kimball models in 1,2 and infinite dimensions, considering either fermions or hard-core bosons. In particular we want to show the very rich structure that these models exhibit and to point out the analogies and differences associated with the statistic of the quantum particles and the nature of the lattice (bipartite or not). The flux phase problem is also discussed.