Fractionally Charged Polarons and Phase Separation in an Extended   Falicov-Kimball Model
  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. 
P. M. R. Brydon, J.-X. Zhu and A. R. Bishop