  We calculate the quantum phase diagram of an extended Falicov-Kimball model
for one and two-dimensional systems in the intermediate coupling regime. Even
though some features of the phase diagram are obtained analytically, the main
results are calculated with a constrained path Monte Carlo technique. We find
that this regime is dominated by a Bose-Einstein condensation of excitons with
a built-in electric polarization. The inclusion of a finite hybridization
between the bands removes the condensate but reinforces the ferroelectricity.
