Critical behavior of the Anderson model on the Bethe lattice via a large-deviation approach

TL;DR

This paper introduces a novel large-deviation method to analyze the Anderson model on the Bethe lattice, accurately characterizing the distribution of local density of states near the localization transition.

Contribution

The authors develop a new large-deviation approach that enables precise analysis of the LDoS distribution tails and correlation volume divergence near the Anderson transition.

Findings

Distribution tails of LDoS can be studied down to probabilities of 10^{-50}

Correlation volume diverges exponentially approaching the transition

Results agree with supersymmetric analytic predictions

Abstract

We present a new large-deviation approach to investigate the critical properties of the Anderson model on the Bethe lattice close to the localization transition in the thermodynamic limit. Our method allows us to study accurately the distribution of the local density of states (LDoS) down to very small probability tails as small as $10^{-50}$ which are completely out of reach for standard numerical techniques. We perform a thorough analysis of the functional form and of the tails of the probability distribution of the LDoS which yields for the first time a direct, transparent, and precise estimation of the correlation volume close to the Anderson transition. Such correlation volume is found to diverge exponentially when the localization is approached from the delocalized regime, in a singular way that is in agreement with the analytic predictions of the supersymmetric treatment.