Influence of Hybridization on the Properties of the Spinless Falicov-Kimball Model

TL;DR

This paper investigates how hybridization affects the ground state properties of the spinless Falicov-Kimball model, showing stability of charge-density waves under small hybridization and clarifying the absence of ferroelectric states.

Contribution

It demonstrates that the inhomogeneous charge-density wave state remains stable with small hybridization using Hartree-Fock approximation, extending understanding of the model's behavior.

Findings

Charge-density wave remains stable for hybridization V < V_c

No ferroelectric ground state with spontaneous polarization

Exact solution for high-dimensional case extended to small hybridization

Abstract

Without a hybridization between the localized f- and the conduction (c-) electron states the spinless Falicov-Kimball model (FKM) is exactly solvable in the limit of high spatial dimension, as first shown by Brandt and Mielsch. Here I show that at least for sufficiently small c-f-interaction this exact inhomogeneous ground state is also obtained in Hartree-Fock approximation. With hybridization the model is no longer exactly solvable, but the approximation yields that the inhomogeneous charge-density wave (CDW) ground state remains stable also for finite hybridization V smaller than a critical hybridization V_c, above which no inhomogeneous CDW solution but only a homogeneous solution is obtained. The spinless FKM does not allow for a ''ferroelectric'' ground state with a spontaneous polarization, i.e. there is no nonvanishing $<c^{\dagger}f>$-expectation value in the limit of vanishing hybridization.