Critical parameters from generalised multifractal analysis at the Anderson transition

TL;DR

This paper introduces a generalized multifractal analysis method for the Anderson transition that characterizes critical behavior solely through wavefunction amplitude distributions, enabling precise estimation of critical parameters without transport measurements.

Contribution

The authors develop a new multifractal analysis approach applicable at the Anderson transition, allowing critical parameters to be extracted from wavefunction statistics alone.

Findings

Estimated critical exponent ν=1.58±0.03

Validated method with high-precision wavefunction data

Characterized transition using probability distribution behavior

Abstract

We propose a generalization of multifractal analysis that is applicable to the critical regime of the Anderson localization-delocalization transition. The approach reveals that the behavior of the probability distribution of wavefunction amplitudes is sufficient to characterize the transition. In combination with finite-size scaling, this formalism permits the critical parameters to be estimated without the need for conductance or other transport measurements. Applying this method to high-precision data for wavefunction statistics obtained by exact diagonalization of the three-dimensional Anderson model, we estimate the critical exponent $\nu=1.58\pm 0.03$.