The geometrically-averaged density of states as a measure of localization

TL;DR

This paper investigates the geometrically averaged density of states as a potential indicator of localization in disordered electron systems, highlighting its limitations and complexities in finite and infinite systems.

Contribution

It critically assesses the effectiveness of the geometrically averaged density of states as an order parameter for the Anderson transition, considering finite-size effects and non-uniqueness issues.

Findings

Finite energy resolution complicates measurements.

Decline in $ ho_g()$ is not solely indicative of localization.

Finite and infinite system behaviors differ in $ ho_g()$ analysis.

Abstract

Motivated by current interest in disordered systems of interacting electrons, the effectiveness of the geometrically averaged density of states, $\rho_g(\omega)$, as an order parameter for the Anderson transition is examined. In the context of finite-size systems we examine complications which arise from finite energy resolution. Furthermore we demonstrate that even in infinite systems a decline in $\rho_g(\omega)$ with increasing disorder strength is not uniquely associated with localization.