Phase space signatures of the Anderson transition

TL;DR

This paper employs phase space analysis using the Husimi function to study the Anderson transition, revealing how quantum states' features persist in phase space and linking delocalization-localization transitions to momentum state coupling.

Contribution

It introduces a phase space approach to analyze the Anderson model, providing new insights into the metal-insulator transition through the Husimi function and inverse participation ratio.

Findings

Quantum states remain observable in phase space at large system sizes.

Delocalization-localization transition relates to coupling of distant momentum eigenstates.

Results align with recent findings in the Aubry-Andre model.

Abstract

We use the inverse participation ratio based on the Husimi function to perform a phase space analysis of the Anderson model in one, two, and three dimensions. Important features of the quantum states remain observable in phase space in the large system size limit, while they would be lost in a real or momentum space description. From perturbative approaches in the limits of weak and strong disorder, we find that the appearance of a delocalization-localization transition is connected to the coupling, by a weak potential, of momentum eigenstates which are far apart in momentum space. This is consistent with recent results obtained for the Aubry-Andre model and provides a novel view on the metal-insulator transition.