Extended Falicov-Kimball model: exact solution for the ground state

TL;DR

This paper provides an exact analysis of the ground state of the extended Falicov-Kimball model, revealing phase transitions, insulating behavior at zero temperature, and metallicity at finite temperatures, with implications for strongly correlated systems.

Contribution

It presents an exact solution for the ground state of the extended Falicov-Kimball model, including phase diagram determination and comparison of mean-field methods.

Findings

Discontinuous transition between charge-ordered phases.

Ground state is insulating at zero temperature.

System can become metallic at finite temperatures.

Abstract

The extended Falicov-Kimball model is analyzed exactly in the ground state at half filling in the limit of large dimensions. In the model the on-site and the intersite density-density interactions between all particles are included. We determined the model's phase diagram and found a discontinuous transition between two different charge-ordered phases. Our analytical calculations show that the ground state of the system is insulating for any nonzero values of the interaction couplings. We also show that the dynamical mean-field theory and the static broken-symmetry Hartree-Fock mean-field approximation give the same results for the model at zero temperature. In addition, we prove using analytical expressions that at infinitesimally small, but finite, temperatures the system can be metallic.