Charge ordering and nonlocal 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 nonlocal 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.