Generalized Inverse Participation Ratio as a Possible Measure of Localization for Interacting Systems

TL;DR

This paper evaluates a generalized inverse participation ratio (GIPR) based on local density of states as a potential measure of Anderson localization in many-body systems, validated through finite-size scaling analysis.

Contribution

It introduces and tests the GIPR as a novel localization measure applicable to interacting systems, aligning well with known critical parameters.

Findings

GIPR effectively distinguishes localized and delocalized phases.

Critical disorder and exponents match established values.

GIPR is suitable for many-body localization studies.

Abstract

We test the usefulness of a generalized inverse participation ratio (GIPR) as a measure of Anderson localization. The GIPR differs from the usual inverse participation ratio in that it depends on the local density of states rather than on the single-electron wavefunctions. This makes it suitable for application to many-body systems. We benchmark the GIPR by performing a finite-size scaling analysis of a disordered, noninteracting, three-dimensional tight-binding lattice. We find values for the critical disorder and critical exponents that are in agreement with published values.