Entanglement Entropy in Scalar Field Theory

TL;DR

This paper calculates how entanglement entropy in interacting scalar field theories depends on the renormalized mass, revealing finite, renormalized contributions and an area law, with implications for quantum phase transitions.

Contribution

It provides a perturbative calculation of entanglement entropy in interacting scalar fields, incorporating renormalization effects and extending previous free theory results.

Findings

Finite, renormalized entanglement entropy up to two-loop order.

The entropy follows an area law with a mass-dependent term.

Renormalized mass replaces bare mass in entropy expressions.

Abstract

Understanding the dependence of entanglement entropy on the renormalized mass in quantum field theories can provide insight into phenomena such as quantum phase transitions, since the mass varies in a singular way near the transition. Here we perturbatively calculate the entanglement entropy in interacting scalar field theory, focussing on the dependence on the field's mass. We study lambda phi^4 and g phi^3 theories in their ground state. By tracing over a half space, using the replica trick and position space Green's functions on the cone, we show that space-time volume divergences cancel and renormalization can be consistently performed in this conical geometry. We establish finite contributions to the entanglement entropy up to two-loop order, involving a finite area law. The resulting entropy is simple and intuitive: the free theory result in d=3 (that we included in an earlier publication) Delta S ~ A m^2 ln(m^2) is altered, to leading order, by replacing the bare mass m by the renormalized mass m_r evaluated at the renormalization scale of zero momentum.