Phase separation in strongly correlated electron systems with wide and   narrow bands: a comparison of the Hubbard-I and DMFT approximations
  The spinless Falicov-Kimball model on the simple cubic lattice is analyzed in the Hubbard-I and dynamical mean field (DMFT) approximations. The Matsubara and real frequency itinerant electron Green's functions, the evolution of the system with doping, and the range of phase separation are found in two approximations. At large values of the on-site Coulomb repulsion both approximations give similar results. The phase separation can be also favorable for a more general model, where heavy electrons have a finite bandwidth. This indicates that the phase separation phenomenon is an inherent feature of the systems described by the Hubbard-like models with wide and narrow bands. 
A.O. Sboychakov
cond-mat.str-el