Critical level statistics and anomalously localized states at the Anderson transition

TL;DR

This paper investigates the level-spacing distribution at the Anderson transition, revealing that anomalously localized states do not alter the critical distribution due to their multifractal tail structures.

Contribution

It demonstrates that anomalously localized states do not influence the critical level-spacing distribution because of their multifractal tail structures.

Findings

ALS do not affect the shape of $P(s)$ at criticality.

$P(s)$ for ALS matches that for typical multifractal states.

Multifractality in ALS tails explains insensitivity of $P(s)$.

Abstract

We study the level-spacing distribution function $P(s)$ at the Anderson transition by paying attention to anomalously localized states (ALS) which contribute to statistical properties at the critical point. It is found that the distribution $P(s)$ for level pairs of ALS coincides with that for pairs of typical multifractal states. This implies that ALS do not affect the shape of the critical level-spacing distribution function. We also show that the insensitivity of $P(s)$ to ALS is a consequence of multifractality in tail structures of ALS.