We present a theory for disordered interacting electrons that can describe both the Mott and Anderson transitions in the respective limits of zero disorder and zero interaction. We use it to investigate the
T=0 Mott-Anderson transition at a fixed electron density, as the disorder strength is increased. Surprisingly, we find two critical values of disorder
Wnfl and
Wc. For
W>Wnfl, the system enters a ``Griffiths'' phase, displaying metallic non-Fermi liquid behavior. At even stronger disorder,
W=Wc>Wnfl the system undergoes a metal-insulator transition, characterized by the linear vanishing of both the typical density of states and the typical quasiparticle weight.
The effects of disorder are investigated in strongly correlated electronic systems near the Mott metal-insulator transition. Correlation effects are found1 to lead to strong disorder screening, a mechanism restricted to low-lying electronic states, very similar to what is observed in underdoped cuprates. These results suggest, however, that this effect is not specific to disordered d-wave superconductors, but is a generic feature of all disordered Mott systems. In addition, the resulting spatial inhomogeneity rapidly increases2 as the Mott insulator is approached at fixed disorder strength. This behavior, which can be described as an Electronic Griffiths Phase, displays all the features expected for disorder-dominated Infinite-Randomness Fixed Point scenario of quantum criticality.