Free Fermions Violate the Area Law For Entanglement Entropy

TL;DR

This paper demonstrates that free fermions exhibit entanglement entropy growth surpassing the boundary area, challenging conventional area law expectations and providing a simplified expression for the leading behavior.

Contribution

It proves a special case of Widom's conjecture, revealing that free fermions violate the traditional area law for entanglement entropy.

Findings

Entanglement entropy grows faster than boundary area.

Provides a simple expression for the leading behavior.

Confirms violation of the area law in free fermions.

Abstract

We show that the entanglement entropy associated to a region grows faster than the area of its boundary surface. This is done by proving a special case of a conjecture due to Widom that yields a surprisingly simple expression for the leading behaviour of the entanglement entropy.