Phase separation in the particle-hole asymmetric Hubbard model
  The paramagnetic phase diagram of the Hubbard model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping on the Bethe lattice is computed at half-filling and in the weakly doped regime using the self-energy functional approach for dynamical mean-field theory. NNN hopping breaks the particle-hole symmetry and leads to a strong asymmetry of the electron-doped and hole-doped regimes. Phase separation occurs at and near half-filling, and the critical temperature of the Mott transition is strongly suppressed. 
M. Eckstein, M. Kollar, M. Potthoff, D. Vollhardt