  We study the effect of strong correlations on the zero bias anomaly (ZBA) in
disordered interacting systems. We focus on the two-dimensional extended
Anderson-Hubbard model, which has both on-site and nearest-neighbor
interactions on a square lattice. We use a variation of dynamical mean field
theory in which the diagonal self-energy is solved self-consistently at each
site on the lattice for each realization of the randomly-distributed disorder
potential. Since the ZBA occurs in systems with both strong disorder and strong
interactions, we use a simplified atomic-limit approximation for the diagonal
inelastic self-energy that becomes exact in the large-disorder limit. The
off-diagonal self-energy is treated within the Hartree-Fock approximation. The
validity of these approximations is discussed in detail. We find that strong
correlations have a significant effect on the ZBA at half filling, and enhance
the Coulomb gap when the interaction is finite-ranged.
