The geometrically-averaged density of states calculated from the local Green's function as a measure of localization

TL;DR

This paper investigates how the geometrically-averaged density of states derived from the local Green's function can serve as a measure of localization in disordered interacting systems, emphasizing the importance of finite energy resolution.

Contribution

It introduces a finite-energy-resolution approach to measure localization, highlighting the significance of energy resolution in the geometrically-averaged density of states.

Findings

Finite energy resolution affects the measurement of localization.

The geometrically-averaged density of states is sensitive to energy resolution.

No limit exists where finite energy resolution becomes irrelevant.

Abstract

With the goal of measuring localization in disordered interacting systems, we examine the finite-size scaling of the geometrically-averaged density of states calculated from the local Green's function with finite energy resolution. Our results show that, unlike in a simple energy binning procedure, there is no limit in which the finite energy resolution is irrelevant.