Typical medium theory of Anderson localization: A local order parameter approach to strong-disorder effects

Abstract

We present a self-consistent theory of Anderson localization that yields a\nsimple algorithm to obtain \\emph{typical local density of states} as an order\nparameter, thereby reproducing the essential features of a phase-diagram of\nlocalization-delocalization quantum phase transition in the standard lattice\nmodels of disordered electron problem. Due to the local character of our\ntheory, it can easily be combined with dynamical mean-field approaches to\nstrongly correlated electrons, thus opening an attractive avenue for a genuine\n{\\em non-perturbative} treatment of the interplay of strong interactions and\nstrong disorder.\n