Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class

TL;DR

This paper employs multifractal finite-size scaling to precisely analyze the Anderson transition in the unitary class, revealing scale invariance and providing accurate critical parameters through extensive numerical simulations.

Contribution

It introduces high-precision numerical estimates of critical exponents and multifractal properties for the Anderson transition in the unitary symmetry class using large-scale simulations.

Findings

Critical exponent of localization length: ν=1.446

Scale invariance of wavefunction intensity distribution at criticality

Accurate estimates of disorder strength and multifractal exponents

Abstract

We use multifractal finite-size scaling to perform a high-precision numerical study of the critical properties of the Anderson localization-delocalization transition in the unitary symmetry class, considering the Anderson model including a random magnetic flux. We demonstrate the scale invariance of the distribution of wavefunction intensities at the critical point and study its behavior across the transition. Our analysis, involving more than $4\times10^6$ independently generated wavefunctions of system sizes up to $L^3=150^3$, yields accurate estimates for the critical exponent of the localization length, $\nu=1.446 (1.440,1.452)$, the critical value of the disorder strength and the multifractal exponents.