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Massive Corrections to Entanglement in Minimal E8 Toda Field Theory

by Olalla A. Castro-Alvaredo

Submission summary

As Contributors: Olalla Castro-Alvaredo
Arxiv Link: http://arxiv.org/abs/1610.07040v2 (pdf)
Date accepted: 2017-02-24
Date submitted: 2017-02-09 01:00
Submitted by: Castro-Alvaredo, Olalla
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory
Approach: Theoretical

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.

Ontology / Topics

See full Ontology or Topics database.

Entanglement Minimal E8 Toda field theory Rényi entropy Twist fields von Neumann entropy

Published as SciPost Phys. 2, 008 (2017)



List of changes

Sections 4 and 5 of the paper have been largely rewritten to make the discussion and conclusions clearer.


Reports on this Submission

Anonymous Report 2 on 2017-2-18 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1610.07040v2, delivered 2017-02-18, doi: 10.21468/SciPost.Report.83

Strengths

See report 1

Weaknesses

See report 1

Report

The author has addressed all the main points I raised in my previous review. i recommend the present manuscript for publication.

Requested changes

None

  • validity: high
  • significance: good
  • originality: high
  • clarity: high
  • formatting: good
  • grammar: good

Anonymous Report 1 on 2017-2-14 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1610.07040v2, delivered 2017-02-14, doi: 10.21468/SciPost.Report.79

Strengths

See my comments on version 1

Weaknesses

See my comments on version 1

Report

The author has addressed my earlier concerns and the conclusions are much clearer in the new version of the paper. I would be happy to now recommend publication.

Requested changes

None

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: good
  • grammar: reasonable

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