Massive Corrections to Entanglement in Minimal E8 Toda Field Theory

TL;DR

This paper clarifies the nature of exponentially decaying corrections to the second Rényi entropy in minimal E8 Toda field theory, correcting previous numerical findings and confirming the expected universal form of the leading correction.

Contribution

The study provides an exact form factor computation showing the leading correction to the second Rényi entropy is proportional to K0(m1 L), correcting earlier numerical results.

Findings

Leading correction proportional to K0(m1 L) confirmed

Previous numerical results suggesting exp(-2m1 L) are shown to be incorrect

Exact form factor calculations clarify the universal behavior of entanglement corrections

Abstract

In this letter we study the exponentially decaying corrections to saturation of the second R\'enyi entropy of one interval of length L in minimal E8 Toda field theory. It has been known for some time that the entanglement entropy of a massive quantum field theory in 1+1 dimensions saturates to a constant value for m1 L <<1 where m1 is the mass of the lightest particle in the spectrum. Subsequently, results by Cardy, Castro-Alvaredo and Doyon have shown that there are exponentially decaying corrections to this behaviour which are characterised by Bessel functions with arguments proportional to m1 L. For the von Neumann entropy the leading correction to saturation takes the precise universal form -K0(2m1 L)/8 whereas for the R\'enyi entropies leading corrections which are proportional to K0(m1 L) are expected. Recent numerical work by P\'almai for the second R\'enyi entropy of minimal E8 Toda has found next-to-leading order corrections decaying as exp(-2m1 L) rather than the expected exp(-m1 L). In this paper we investigate the origin of this result and show that it is incorrect. An exact form factor computation of correlators of branch point twist fields reveals that the leading corrections are proportional to K0(m1 L) as expected.