  Several recent exact diagonalization calculations have established that the
Anderson-Hubbard model has a disorder-induced zero bias anomaly (ZBA) (also
called a disorder-induced pseudogap) in the density of states. In order to
understand the physics of the ZBA, we study a simplified problem---an ensemble
of two-site molecules with random site energies---for which analytical results
are possible. For this ensemble, we examine how the ZBA forms in both the
weakly correlated (mean field) and strongly correlated limits. In the weakly
correlated case, the ZBA can be understood as the result of level repulsion
between bonding and antibonding molecular orbitals. A similar level repulsion
occurs in the strongly correlated case too, but a larger contribution to the
ZBA comes from the suppression of a triplet excitation mode. This inherently
many-body mechanism does not have a counterpart in mean-field models.
