Scaling of Level Statistics at the Disorder-Induced Metal-Insulator Transition

TL;DR

This paper numerically investigates the energy level statistics at the Anderson metal-insulator transition, demonstrating one-parameter scaling and determining critical parameters with high precision.

Contribution

It provides a detailed numerical analysis of level statistics at the transition, establishing universality and accurately estimating critical disorder and exponent.

Findings

Critical disorder W_c = 16.35 identified

Critical exponent ν = 1.45 ± 0.08 measured

Evidence of one-parameter scaling in level statistics

Abstract

The distribution of energy level separations for lattices of sizes up to 28$\times$28$\times$28 sites is numerically calculated for the Anderson model. The results show one-parameter scaling. The size-independent universality of the critical level spacing distribution allows to detect with high precision the critical disorder $W_{c}=16.35$. The scaling properties yield the critical exponent, $\nu =1.45 \pm 0.08$, and the disorder dependence of the correlation length.