  Using a combination of numerical and analytical calculations, we study the
disorder-induced zero bias anomaly (ZBA) in the density of states of
strongly-correlated systems modeled by the two dimensional Anderson-Hubbard
model. We find that the ZBA comes from the response of the nonlocal inelastic
self-energy to the disorder potential, a result which has implications for
theoretical approaches that retain only the local self-energy. Using an
approximate analytic form for the self-energy, we derive an expression for the
density of states of the two-site Anderson-Hubbard model. Our formalism
reproduces the essential features of the ZBA, namely that the width is
proportional to the hopping amplitude $t$ and is independent of the interaction
strength and disorder potential.
