Abstract:
In this seminar, a model of noninteracting disordered electrons is studied in high spatial dimensions in order to develop a mean-field description of Anderson localization transition. Off-diagonal one- and two-particle propagators are found to behave as Gaussian random variables with respect to momentum summations. With this simplification the parquet equations for two-particle irreducible vertices are reduced to an algebraic equation for a single local quantity. The time-reversal invariance, displayed as the electron-hole symmetry of two-particle functions, plays a substantial role in such a reduction as well. We find a disorder-driven bifurcation point in the resulting equation that signals vanishing of diffusion and onset of Anderson localization.