Analysis of localization-delocalization transitions in corner-sharing tetrahedral lattices

TL;DR

This paper investigates the Anderson localization-delocalization transition in corner-sharing tetrahedral lattices using three numerical methods, providing precise critical parameters and confirming previous findings with improved accuracy.

Contribution

It introduces a comprehensive multi-method analysis of the transition, accurately estimating critical disorder, energy, and exponent with advanced error analysis.

Findings

Critical disorder Wc=14.474(8) at Ec=-4.0

Critical exponent ν=1.565(11)

High agreement among methods and improved accuracy

Abstract

We study the critical behavior of the Anderson localization-delocalization transition in corner-sharing tetrahedral lattices. We compare our results obtained by three different numerical methods namely the multifractal analysis, the Green resolvent method, and the energy-level statistics which yield the singularity strength, the decay length of the wave functions, and the (integrated) energy-level distribution, respectively. From these measures a finite-size scaling approach allows us to determine the critical parameters simultaneously. With particular emphasis we calculate the propagation of the statistical errors by a Monte-Carlo method. We find a high agreement between the results of all methods and we can estimate the highest critical disorder $W_\mathrm{c}=14.474(8)$ at energy $E_\mathrm{c}=-4.0$ and the critical exponent $\nu=1.565(11)$. Our results agree with a previous study by Fazileh et al. but improve accuracy significantly.