One Dimensional Continuum Falicov-Kimball Model in the Strongly Correlated Limit

TL;DR

This paper investigates the thermodynamics of a one-dimensional continuum Falicov-Kimball model in the strongly correlated limit, revealing electron clustering and phase transitions influenced by repulsive interactions.

Contribution

It introduces a continuum analogue of the Falicov-Kimball model and analyzes its ground state configurations and phase transitions using a method adapted from the Takahashi gas.

Findings

F electrons form clusters in the ground state

Increasing Takahashi repulsion causes a transition to a homogeneous configuration

Discontinuous change in electron arrangement observed with varying repulsion

Abstract

In this paper we study the thermodynamics of the one dimensional continuum analogue of the Falicov-Kimball model in the strongly correlated limit using a method developed by Salsburg, Zwanzig and Kirkwood for the Takahashi gas. In the ground state it is found that the $f$ electrons form a cluster. The effect of including a Takahashi repulsion between $f$ particles is also studied where it is found that as the repulsion is increased the ground state $f$ electron configuration changes discontinuously from the clustered configuration to a homogeneous or equal spaced configuration analogous to the checkerboard configuration which arises in the lattice Falicov-Kimball model.