Weak-coupling Treatment of Electronic (Anti-)Ferroelectricity in the Extended Falicov-Kimball Model

TL;DR

This paper investigates the weak-coupling behavior of the extended Falicov-Kimball model in infinite dimensions, revealing phase transitions among charge-density wave, ferroelectric, and antiferroelectric states based on model parameters and temperature.

Contribution

It introduces a weak-coupling analytical approach to the extended Falicov-Kimball model, exploring phase stability and transitions in infinite dimensions.

Findings

First-order transition from CDW to EFE/EAFE phases

Phase diagrams showing stability regions of different orders

Calculation of order parameters and total energy

Abstract

We study the (spinless) Falicov-Kimball model extended by a finite band width (hopping $t_f$) of the localized (f-) electrons in infinite dimensions in the weak-coupling limit of a small local interband Coulomb correlation $U$ for half filling. In the case of overlapping conduction- and f-bands different kinds of ordered solutions are possible, namely charge-density wave (CDW) order, electronic ferroelectricity (EFE) and electronic antiferroelectricity (EAFE). The order parameters are calculated as a function of the model parameters and of the temperature. There is a first-order phase transition from the CDW-phase to the EFE- or EAFE-phase. The total energy is calculated to determine the thermodynamically stable solution. The quantum phase diagrams are calculated.