Entanglement between quantum fields

TL;DR

This paper investigates quantum entanglement between interacting fields using Rènyi entropy, revealing larger entanglement in symmetry-broken states and proposing entanglement as a signature for unobserved fields like the Higgs sector.

Contribution

It introduces a method to quantify field entanglement with Rènyi entropy and generalizes the geometric entropy area law for quantum fields.

Findings

Entanglement is greater in spontaneously broken symmetry states.

A generalized geometric entropy area law is derived.

Entanglement can indicate the presence of unobserved fields.

Abstract

We analyze entanglement between quantum interacting fields. In particular, we use R\'enyi entropy to quantify the entanglement between the fields in the ground state of the linear $\sigma$ model. We adopt R\'enyi entropy because the failure of the replica trick method does not permit to obtain the Von Neumann entropy. We find that the degree of entanglement is larger in the spontaneously broken symmetry case and a generalization of geometric entropy area law is obtained. Finally, we suggest that entanglement between fields can be used as a signature of the presence of unobserved fields, such as is the Higgs model case with its unobserved sector.