Anticorrelations from power-law spectral disorder and conditions for an Anderson transition

TL;DR

This paper clarifies the conditions under which power-law spectral disorder leads to Anderson transitions, showing that anticorrelations in the thermodynamic limit reconcile numerical and analytical results.

Contribution

It demonstrates that strong anticorrelations in spectral disorder enable Anderson transitions, resolving previous contradictions between numeric and analytic findings.

Findings

Anticorrelations in spectral disorder are key to Anderson transitions.

Scaling functions indicate size-dependent disorder smoothing.

No contradiction exists between numeric and analytic results when anticorrelations are considered.

Abstract

We resolve an apparent contradiction between numeric and analytic results for one-dimensional disordered systems with power-law spectral correlations. The conflict arises when considering rigorous results that constrain the set of correlation functions yielding metallic states to those with non-zero values in the thermodynamic limit. By analyzing the scaling law for a model correlated disorder that produces a mobility edge, we show that no contradiction exists as the correlation function exhibits strong anticorrelations in the thermodynamic limit. Moreover, the associated scaling function reveals a size-dependent correlation with a smoothening of disorder amplitudes as the system size increases.