Charge-ordered state from weak to strong coupling

We apply the dynamical mean field theory to the problem of charge ordering. In this framework we solve the Holstein model for electrons interacting wi th classical phonons in the case of a bipartite lattice. The calculations h as been done at all fillings and temperatures. In the normal state, as well as in the charge-ordered (CO) state, the existence of polarons, i.e., elec trons strongly coupled to local lattice deformation, is associated to the q ualitative behavior of the lattice displacement probability distribution fu nction (LDPDF). Properties of the CO state are qualitatively different in w eak and strong coupling. The weak-coupling regime is characterized by a sin gle-peak LDPDF centered on the sublattice average polarization. The strong- coupling regime is characterized by a double-peak nonsymmetric LDPDF. The s econdary peak is centered on the average polarization of the other sublatti ce indicating a certain amount of defects in the ordered state. This regime can be interpreted as that of a CO phase resulting from the spatial orderi ng of preexisting randomly distributed polarons. The CO critical temperatur e exhibits a maximum in the normal to polaron crossover region. [S0163-1829 (99)00507-X].