Determination of the mobility edge in the Anderson model of localization in three dimensions by multifractal analysis

Abstract

We study the Anderson model of localization in three dimensions with different probability distributions for the site energies. Using the Lanczos algorithm we calculate eigenvectors for different model parameters like disorder and energy. From these we derive the singularity spectrum typically used for the characterization of multifractal objects. We demonstrate that the singularity spectrum at the critical disorder, which determines the mobility edge at the band center, is independent of the employed probability distribution. Assuming that this singularity spectrum is universal for the metal-insulator transition regardless of specific parameters of the model we establish a straightforward method to distinguish localized and extended states. In this way we obtain the entire mobility-edge trajectory separating regions of extended states from regions of localized states in the energy-disorder phase diagram. The good agreement with results from transfer-matrix calculations for all probability distributions used corroborates the applicability of our criterion.