Charge-density-wave order parameter of the Falicov-Kimball model in infinite dimensions

TL;DR

This paper investigates the behavior of the charge-density-wave order parameter in the Falicov-Kimball model across different interaction strengths, revealing anomalous temperature dependence and crossover phenomena in infinite dimensions.

Contribution

It provides a numerical study of the order parameter crossover from BCS-like to non-BCS-like behavior in the Falicov-Kimball model.

Findings

Order parameter exhibits anomalous temperature dependence.

Crossover between BCS-like and non-BCS-like regimes identified.

Qualitative characterization of the order parameter across U values.

Abstract

In the large-U limit, the Falicov-Kimball model maps onto an effective Ising model, with an order parameter described by a BCS-like mean-field theory in infinite dimensions. In the small-U limit, van Dongen and Vollhardt showed that the order parameter assumes a strange non-BCS-like shape with a sharp reduction near T approx T_c/2. Here we numerically investigate the crossover between these two regimes and qualitatively determine the order parameter for a variety of different values of U. We find the overall behavior of the order parameter as a function of temperature to be quite anomalous.