Analysis of the Disorder-Induced Zero Bias Anomaly in the Anderson-Hubbard Model

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.