New class of level statistics in correlated disordered chains

TL;DR

This paper investigates how long-range correlations in 1D disordered systems influence their energy level statistics, revealing a threshold in correlation strength that leads to a new class of statistical distributions.

Contribution

The study identifies a critical correlation threshold in 1D disordered systems where the level statistics transition from Poisson to a new class of distributions, introducing a novel understanding of correlated disorder effects.

Findings

Poisson distribution for low correlations

New class of level statistics above the threshold

Standard deviation converges to Poisson value at the threshold

Abstract

We study the properties of the level statistics of 1D disordered systems with long-range spatial correlations. We find a threshold value in the degree of correlations below which in the limit of large system size the level statistics follows a Poisson distribution (as expected for 1D uncorrelated disordered systems), and above which the level statistics is described by a new class of distribution functions. At the threshold, we find that with increasing system size the standard deviation of the function describing the level statistics converges to the standard deviation of the Poissonian distribution as a power law. Above the threshold we find that the level statistics is characterized by different functional forms for different degrees of correlations.