Numerical investigations of scaling at the Anderson transition

TL;DR

This paper reviews numerical studies of the Anderson transition, focusing on finite-size scaling techniques to accurately analyze the metal-insulator transition in disordered systems at low temperatures.

Contribution

It demonstrates the application of high-precision numerical methods and finite-size scaling to investigate the Anderson transition and effects of interactions in disordered solids.

Findings

Finite-size scaling enables reliable estimates of the transition point.

Disorder can induce a transition from conducting to insulating behavior.

Numerical methods improve understanding of localization phenomena.

Abstract

At low temperature T, a significant difference between the behavior of crystals on the one hand and disordered solids on the other is seen: sufficiently strong disorder can give rise to a transition of the transport properties from conducting behavior with finite resistance R to insulating behavior with R=infinity as T -> 0. This well-studied phenomenon is called the disorder-driven metal-insulator transition and it is characteristic to non-crystalline solids. In this review of recent advances, we have presented results of transport studies in disordered systems, ranging from modifications of the standard Anderson model of localization to effects of a two-body interaction. Of paramount importance in these studies was always the highest possible accuracy of the raw data combined with the careful subsequent application of the finite-size scaling technique. In fact, it is this scaling method that has allowed numerical studies to move beyond simple extrapolations and reliably construct estimates of quantities as if one were studying an infinite system.