Is Renormalized Entanglement Entropy Stationary at RG Fixed Points?

TL;DR

This paper investigates whether the renormalized entanglement entropy (REE) remains stationary at RG fixed points, finding through numerical analysis that REE is not stationary at the UV fixed point in free scalar field theory.

Contribution

It provides a numerical study showing REE is not stationary at the UV fixed point, challenging assumptions about its behavior at conformal fixed points.

Findings

REE is not stationary at the UV fixed point.

Numerical calculations support non-stationarity of REE.

Results suggest reevaluation of REE as a c-function at fixed points.

Abstract

The renormalized entanglement entropy (REE) across a circle of radius R has been proposed as a c-function in Poincar\'e invariant (2+1)-dimensional field theory. A proof has been presented of its monotonic behavior as a function of R, based on the strong subadditivity of entanglement entropy. However, this proof does not directly establish stationarity of REE at conformal fixed points of the renormalization group. In this note we study the REE for the free massive scalar field theory near the UV fixed point described by a massless scalar. Our numerical calculation indicates that the REE is not stationary at the UV fixed point.