Order, criticality and excitations in the extended Falicov-Kimball model

TL;DR

This paper uses exact numerical methods to explore excitonic states and coherence in a one-dimensional extended Falicov-Kimball model, revealing a Coulomb-driven BCS-BEC crossover and spectral features consistent with experimental observations.

Contribution

It provides a detailed numerical analysis of excitonic phases and the BCS-BEC crossover in the extended Falicov-Kimball model, highlighting the effects of mass imbalance and spectral properties.

Findings

Identification of an excitonic insulator with power-law correlations.

Demonstration of a Coulomb-driven BCS-BEC crossover.

Observation of a flat valence-band top in the BEC regime.

Abstract

Using exact numerical techniques we investigate the nature of excitonic (electron-hole) bound states and the development of exciton coherence in the one-dimensional half-filled extended Falicov-Kimball model. The ground-state phase diagram of the model exhibits, besides band insulator and staggered orbital ordered phases, an excitonic insulator (EI) with power-law correlations. The criticality of the EI state shows up in the von Neumann entropy. The anomalous spectral function and condensation amplitude provide the binding energy and coherence length of the electron-hole pairs which, on their part, point towards a Coulomb interaction driven crossover from BCS-like electron-hole pairing fluctuations to tightly bound excitons. We show that while a mass imbalance between electrons and holes does not affect the location of the BCS-BEC crossover regime it favors staggered orbital ordering to the disadvantage of the EI. Within the BEC regime the quasiparticle dispersion develops a flat valence-band top in accord with the experimental finding for Ta$_2$NiSe$_5$.