Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions

TL;DR

This study numerically investigates entanglement entropy in disordered free fermion Anderson models across one to three dimensions, confirming the area law in the metallic phase when the subsystem size exceeds the mean free path.

Contribution

It demonstrates that the entanglement entropy obeys the area law in disordered Anderson models in multiple dimensions, including the metallic phase with finite mean free path.

Findings

Entanglement entropy follows the area law in the Anderson model's metallic phase.

The area law holds when the subsystem size exceeds the mean free path.

Results connect to previous studies on area law violations in special 1D models.

Abstract

We calculate numerically the entanglement entropy of free fermion ground states in one-, two- and three-dimensional Anderson models, and find that it obeys the area law as long as the linear size of the subsystem is sufficiently larger than the mean free path. This result holds in the metallic phase of the three-dimensional Anderson model, where the mean free path is finite although the localization length is infinite. Relation between the present results and earlier ones on area law violation in special one-dimensional models that support metallic phases is discussed.