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Massive Corrections to Entanglement in Minimal E8 Toda Field Theory
by Olalla A. Castro-Alvaredo
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Olalla Castro-Alvaredo |
| Submission information | |
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| Preprint 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 |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| 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.
List of changes
Sections 4 and 5 of the paper have been largely rewritten to make the discussion and conclusions clearer.
Published as SciPost Phys. 2, 008 (2017)
Reports on this Submission
Report #2 by Anonymous (Referee 1) 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
Report #1 by Anonymous (Referee 2) 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