  Using extended dynamical mean-field theory and its combination with the $GW$
approximation, we compute the phase diagrams and local spectral functions of
the single-band extended Hubbard model on the square and simple cubic lattices,
considering long range interactions up to the third nearest neighbors. The
longer range interactions shift the boundaries between the metallic,
charge-ordered insulating and Mott insulating phases, and lead to
characteristic changes in the screening modes and local spectral functions.
Momentum-dependent self-energy contributions enhance the correlation effects
and thus compete with the additional screening effect from longer range Coulomb
interactions. Our results suggest that the influence of longer range intersite
interactions is significant, and that these effects deserve attention in
realistic studies of correlated materials.
