  We present the first numerical study of the Falicov-Kimball model extended by
an on-site hybridization away from the particle-hole symmetry point. Stable
polaronic distortions of the charge-density wave (CDW) phase are observed when
doping with a single hole. For moderate hole-doping, we find phase separation
between a hole-rich homogeneous state and the usual CDW state. Excitonic order
is enhanced around the hole-rich region, locally manifesting the global
competition between this and the CDW phase. Associated with the hole-doping is
a fractionalization of the electron density between the itinerant and localized
electrons. The calculated local density of states at the polaron centre reveals
this fractionalization to be the result of charge fluctuations induced by the
hybridization. We propose a scanning tunneling microscope experiment to test
our results.
