The generalized localization lengths in one dimensional systems with correlated disorder

TL;DR

This paper investigates the scale-invariant properties of wave functions in one-dimensional disordered systems with correlations, introducing generalized localization lengths and suggesting power-law localization may occur.

Contribution

It introduces generalized entropic localization lengths and compares their behavior with exponential localization in correlated disorder models, challenging the oversimplified exponential assumption.

Findings

Generalized entropic localization lengths provide a better characterization of states.

Exponential localization may be insufficient for correlated disorder systems.

Power-law localization cannot be excluded in the studied models.

Abstract

The scale invariant properties of wave functions in finite samples of one dimensional random systems with correlated disorder are analyzed. The random dimer model and its generalizations are considered and the wave functions are compared. Generalized entropic localization lengths are introduced in order to characterize the states and compared with their behavior for exponential localization. An acceptable agreement is obtained, however, the exponential form seems to be an oversimplification in the presence of correlated disorder. According to our analysis in the case of the random dimer model and the two new models the presence of power-law localization cannot be ruled out.