Does the Falicov-Kimball model allow for a ferroelectric ground state with a spontaneous polarization?

TL;DR

This study investigates whether the one-dimensional Falicov-Kimball model can exhibit a ferroelectric ground state with spontaneous polarization, concluding that it does not allow such a state based on exact-diagonalization calculations.

Contribution

The paper provides the first detailed analysis of electronic ferroelectricity in the 1D Falicov-Kimball model using extrapolated small-cluster calculations.

Findings

Neither spinless nor spin-one-half FKM shows ferroelectric ground state.

No nonvanishing <d^{+}f> expectation value at zero hybridization.

Falicov-Kimball model does not support spontaneous polarization.

Abstract

The extrapolation of small-cluster exact-diagonalization calculations is used to examine the possibility of electronic ferroelectricity in the one dimensional spinless and spin-one-half Falicov-Kimball model (FKM). It is found that neither spinless nor spin-one-half version of the FKM does not allow for a ferroelectric ground state with a spontaneous polarization, i.e. there is no nonvanishing $<d^{+}f>$-expectation value for vanishing hybridization $V$.