Multifractality and the distribution of the Kondo temperature at the Anderson transition

TL;DR

This paper numerically investigates the distribution of Kondo temperatures at the Anderson transition, confirming the analytical prediction of a universal power law tail influenced by multifractal wavefunction properties.

Contribution

It provides numerical validation for the analytical approximation of the Kondo temperature distribution's tail at the Anderson transition.

Findings

Distribution has a long tail at small Kondo temperatures

Numerical results support the universal power law tail prediction

Multifractal wavefunction properties influence the distribution

Abstract

Using numerical simulations, we investigate the distribution of Kondo temperatures at the Anderson transition. In agreement with previous work, we find that the distribution has a long tail at small Kondo temperatures. Recently, an approximation for the tail of the distribution was derived analytically. This approximation takes into account the multifractal distribution of the wavefunction amplitudes (in the parabolic approximation), and power law correlations between wave function intensities, at the Anderson transition. It was predicted that the distribution of Kondo temperatures has a power law tail with a universal exponent. Here, we attempt to check that this prediction holds in a numerical simulation of Anderson's model of localisation in three dimensions.