Strong correlations and disorder in d=∞ and beyond

The behavior of strongly correlated electrons in disordered systems is investigated using a functional integral formulation of the problem. In the mean-field approximation, which becomes exact in the limit of large spatial dimensionality, the problem reduces to the solution of an ensemble of self-consistently determined Anderson impurity models. The methods are applied to different classes of disorder, and the possible phases of the system are analyzed. We present results for the behavior of the thermodynamic and transport properties near the metal-insulator transitions for each case considered. When strong hopping disorder is present, disorder-induced local-moment formation is found, leading to qualitative modifications of metallic phases even away from the transition. Finally, we indicate how our approach can be systematically extended beyond the mean-field limit, where the presence of spatial fluctuations makes it possible to address the problem of Anderson localization in strongly correlated electronic systems.