Charge ordering and non-local correlations in the doped extended Hubbard model

We study the extended Hubbard model away from half-filling on a two-dimensional square lattice using cluster dynamical mean field theory on clusters of size $8$. We show that the model exhibits metallic, compressible charge ordered, and insulating charge ordered phases. We determine the location of the charge ordering phase transition line at finite temperature and the properties of the phases as a function of doping, temperature, local interaction, and nearest neighbor interaction. An analysis of the energetics of the charge order transition shows that the charge ordering transition mainly results in a rearrangement of local and non-local potential energy. We show the doping evolution of the spectral function from the isotropic metal via a charge ordered metal to a charge ordered insulator with a big gap, and study finite size effects of the approximation.