An Inverse Mass Expansion for Entanglement Entropy in Free Massive Scalar Field Theory

TL;DR

This paper introduces a perturbative method using inverse mass expansion to calculate entanglement entropy in free massive scalar field theories across multiple dimensions, revealing universal and scheme-dependent terms.

Contribution

It develops a novel perturbative approach based on inverse mass expansion for entanglement entropy, providing spectrum information and insights into the area law's relation to locality.

Findings

Perturbative expansion accurately approximates the area law coefficient.

Method applies to massless scalar fields in higher dimensions.

Spectrum of the reduced density matrix obtained as an intermediate result.

Abstract

We extend the entanglement entropy calculation performed in the seminal paper by Srednicki for free real massive scalar field theories in 1+1, 2+1 and 3+1 dimensions. We show that the inverse of the scalar field mass can be used as an expansion parameter for a perturbative calculation of the entanglement entropy. We perform the calculation for the ground state of the system and for a spherical entangling surface at third order in this expansion. The calculated entanglement entropy contains a leading area law term, as well as subleading terms that depend on the regularization scheme, as expected. Universal terms are non-perturbative effects in this approach. Interestingly, this perturbative expansion can be used to approximate the coefficient of the area law term, even in the case of a massless scalar field in 2+1 and 3+1 dimensions. The presented method provides the spectrum of the reduced density matrix as an intermediate result, which is an important advantage in comparison to the replica trick approach. Our perturbative expansion underlines the relation between the area law and the locality of the underlying field theory.