The effects of the next-nearest-neighbour density–density interaction in the atomic limit ofthe extended Hubbard model

Abstract

We have studied the extended Hubbard model in the atomic limit.The Hamiltonian analysed consists of the effective on-site interactionU and the intersite density–density interactionsWij (both nearest-neighbour and next-nearest-neighbour). The model can be considered asa simple effective model of charge ordered insulators. The phase diagrams andthermodynamic properties of this system have been determined within the variationalapproach, which treats the on-site interaction term exactly and the intersite interactionswithin the mean-field approximation. Our investigation of the general case taking intoaccount for the first time the effects of longer-ranged density–density interaction (repulsiveand attractive) as well as possible phase separations shows that, depending on thevalues of the interaction parameters and the electron concentration, the systemcan exhibit not only several homogeneous charge ordered (CO) phases, but alsovarious phase separated states (CO–CO and CO–nonordered). One finds that themodel considered exhibits very interesting multicritical behaviours and features,including bicritical, tricritical, and critical end points and isolated critical points.