  We present a Hartree-Fock study of the Falicov-Kimball model extended by both
on-site and non-local hybridization. We examine the interplay between excitonic
effects and the charge-density wave (CDW) instability known to exist at zero
hybridization. It is found that the CDW state remains stable in the presence of
finite hybridization; for on-site hybridization the Coulomb interaction
nevertheless strongly enhances the excitonic average above its value in the
noninteracting system. In contrast, for non-local hybridization, we observe no
such enhancement of the excitonic average or a spontaneous on-site
hybridization potential. Instead, we find only a significant suppression of the
excitonic correlations in the CDW state. A phenomenological Ginzburg-Landau
analysis is also provided to understand the interplay.
