Perturbative entanglement entropy in nonlocal theories

TL;DR

This paper investigates whether nonlocal theories exhibit volume law entanglement entropy at weak coupling, finding that to first order, they follow an area law similar to local theories, with implications for understanding entanglement in nonlocal systems.

Contribution

The study provides the first perturbative analysis of entanglement entropy in nonlocal theories, showing they follow an area law at leading order, contrary to expectations of a volume law.

Findings

Nonlocal theories studied follow an area law at first order in coupling.

No evidence of volume law entanglement at weak coupling in these theories.

Perturbative nonlocal interactions do not generate sufficient entanglement to alter the leading divergence.

Abstract

Entanglement entropy in the vacuum state of local field theories exhibits an area law. However, nonlocal theories at large N and strong coupling violate this area law. In these theories, the leading divergence in the entanglement entropy is extensive for regions smaller than the effective nonlocality scale and proportional to this effective nonlocality scale for regions larger than it. This raises the question: is a volume law a generic feature of nonlocal theories, or is it only present at strong coupling and large N? This paper investigates entanglement entropy of large regions in weakly coupled nonlocal theories, to leading order in the coupling. The two theories studied are phi^4 theory on the noncommutative plane and phi^4 theory with a dipole type nonlocal modification using a fixed nonlocality scale. Both theories are found to follow an area law to first order in the coupling, hence no evidence is found for a volume law. This indicates that, perturbatively the nonlocal interactions considered are not generating sufficient entanglement at distances of the nonlocality scale to change the leading divergence, at least to first order in the coupling. An argument against volume laws at higher orders is also presented.