Critical exponent for the Anderson transition in the three dimensional orthogonal universality class

TL;DR

This paper presents a finite size scaling study of the Anderson localization transition in three dimensions, estimating the critical exponent and confirming its universality across different disorder distributions, with relevance to experimental quantum systems.

Contribution

It provides a precise estimation of the critical exponent for the 3D Anderson transition and confirms its universality across multiple disorder distributions.

Findings

Critical exponent estimated accurately for the Anderson transition.

Universality of the critical exponent verified across different disorder types.

Results align with experimental measurements in cold atomic gases.

Abstract

We report a careful finite size scaling study of the metal insulator transition in Anderson's model of localisation. We focus on the estimation of the critical exponent $\nu$ that describes the divergence of the localisation length. We verify the universality of this critical exponent for three different distributions of the random potential: box, normal and Cauchy. Our results for the critical exponent are consistent with the measured values obtained in experiments on the dynamical localisation transition in the quantum kicked rotor realised in a cold atomic gas.