Dynamical mean field theory of the CDW phase

Abstract
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. In the normal state as well as in the Charge Density Wave (CDW) state the existence of polarons, i.e. electrons strongly coupled to local lattice deformation, is associated to the qualitative properties of the Lattice Polarization Distribution Function (LPDF). Properties of the CDW ordered state are qualitatively different in weak and strong coupling. We investigate the cross-over from weak coupling CDW behavior, characterized by a single peak LPDF in each sub-lattice centered on the sub-lattice average polarization, the strong coupling CDW regime which is characterised by a double peak non symmetric LPDF in each sub-lattice. The secondary peak is centered on the average polarization of the other sub-lattice indicating a certain amount of defects in the ordered state. This regime can be interpreted as that of a CDW phase resulting from the spatial ordering of preexisting randomly distributed polarons. The CDW critical temperature exhibits a maximum in the normal-to-polaron crossover region.