  We study the half filled extended Hubbard model on a two-dimensional square
lattice using cluster dynamical mean field theory on clusters of size 8-20. We
show that the model exhibits metallic, Mott insulating, and charge ordered
phases, and determine the location of the charge ordering phase transition line
and the properties of the ordered and disordered phase as a function of
temperature, local interaction, and nearest neighbor interaction. We find
strong non-local correlations in the uniform phase and a pronounced screening
effect in the vicinity of the phase transition, where non-local interactions
push the system towards metallic behavior. In contrast, correlations in the
ordered phase are mostly local to the unit cell. Extrapolation to the
thermodynamic limit and control of all sources of errors allow us to assess the
regime of applicability of simpler approximation schemes for systems with
non-local interactions. We also demonstrate how strong non-local
electron-electron interactions can increase electron mobility by turning a
charge ordered insulator into a metal.
