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 with classical phonons in the case of a bipartite lattice. The calculations has 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., electrons strongly coupled to local lattice deformation, is associated to the qualitative behavior of the lattice displacement probability distribution function (LDPDF). Properties of the CO state are qualitatively different in weak and strong coupling. The weak-coupling regime is characterized by a single-peak LDPDF centered on the sublattice average polarization. The strong-coupling regime is characterized by a double-peak nonsymmetric LDPDF. The secondary peak is centered on the average polarization of the other sublattice 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 ordering of preexisting randomly distributed polarons. The CO critical temperature exhibits a maximum in the normal to polaron crossover region. [S0163-1829(99)00507-X].