Charge Orderings and Phase Separations in the Atomic Limit of the Extended Hubbard Model with Intersite Density-Density Interactions

A simple effective model of charge ordered insulators is studied. The tight binding Hamiltonian consists of the effective on-site interaction U and the intersite density-density interactions W(ij) (both: nearest-neighbour and next-nearest neighbour). In the analysis of the phase diagrams we have adopted the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. The phase separated states have not been taken into account in previous analyses. Our investigations of two cases of the on-site interaction: attraction (U/(-W(Q)) = -10) and repulsion (U/(-W(Q)) = 1.1) show that, depending on the values of the next-nearest neighbour attraction, the system can exhibit not only homogeneous phases: charge ordered and nonordered, but also various phase separated states (charge ordered nonordered, charge ordered charge ordered).