Phase diagram of the asymmetric Hubbard model
  The ground-state phase diagram of the asymmetric Hubbard model is studied in one and two dimensions by a well-controlled numerical method. The method allows to calculate directly the probabilities of particular phases in the approximate ground-state and thus to specify the stability domains corresponding to phases with the highest probabilities. Depending on the electron filling $n$ and the magnitude of the asymmetry $t_f/t_d$ between the hopping integrals of $f$ and $d$ electrons two different scenarios in formation of ground states are observed. At low electron fillings ($n\leq 1/3$) the ground states are always phase segregated in the limit of strong asymmetry ($t_d\gg t_f$). With decreasing asymmetry the system undergoes a transition to the phase separated state and then to the homogeneous state. For electron fillings $n>1/3 $ and weak Coulomb interactions the ground state is homogeneous for all values of asymmetry, while for intermediate and strong interactions the system exhibits the same sequence of phase transitions as for $n$ small. Moreover, it is shown that the segregated phase is significantly stabilized with increasing electron filling, while the separated phases disappear gradually from the ground-state phase diagrams. 
Pavol Farkasovsky