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Entanglement entropy from entanglement contour: higher dimensions

by Muxin Han, Qiang Wen

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Qiang Wen
Submission information
Preprint Link: scipost_202111_00034v2  (pdf)
Date accepted: 2022-03-25
Date submitted: 2022-02-21 06:55
Submitted by: Wen, Qiang
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Gravitation, Cosmology and Astroparticle Physics
  • High-Energy Physics - Theory
  • Quantum Physics
Approach: Theoretical


We study the \textit{entanglement contour} and \textit{partial entanglement entropy} (PEE) in quantum field theories in 3 and higher dimensions. The entanglement entropy is evaluated from a certain limit of the PEE with a geometric regulator. In the context of the \textit{entanglement contour}, we classify the geometric regulators, study their difference from the UV regulators. Furthermore, for spherical regions in conformal field theories (CFTs) we find the exact relation between the UV and geometric cutoff, which clarifies some subtle points in the previous literature. We clarify a subtle point of the additive linear combination (ALC) proposal for PEE in higher dimensions. The subset entanglement entropies in the \textit{ALC proposal} should all be evaluated as a limit of the PEE while excluding a fixed class of local-short-distance correlation. Unlike the 2-dimensional configurations, naively plugging the entanglement entropy calculated with a UV cutoff will spoil the validity of the \textit{ALC proposal}. We derive the \textit{entanglement contour} function for spherical regions, annuli and spherical shells in the vacuum state of general-dimensional CFTs on a hyperplane.

Author comments upon resubmission

We thank the referees for suggestions that help improve the manuscript in various aspects. We have made all changes required by the referees, fixed the typos and improved the presentation.

List of changes

We made the changes required by the referees, including
1, Eq.(10) rewritten
2, subsection 3.1, reference for the Fig deleted.
3, the third point at the beginning of page 11 rewritten
4, paragraph around (41) rewritten
5, clarification added for the validity of (50) and (53)
6, footnote added in page 4
7, footnote added in page 15
8. reference added at the beginning of sec. 6.2
see our reply to the referees for more details.

We changed the title of section 6, added some references and did some minor changes to improve the repsentation.

Published as SciPost Phys. Core 5, 020 (2022)

Reports on this Submission

Anonymous Report 2 on 2022-3-15 (Invited Report)


the same of my previous report


the same of my previous report


The authors have implemented the suggested changes in a satisfactory way. However, I think that the paper is more suitable for Scipost Core rather than Scipost Physics.

  • validity: ok
  • significance: good
  • originality: ok
  • clarity: good
  • formatting: excellent
  • grammar: excellent

Anonymous Report 1 on 2022-3-1 (Invited Report)


I think now the paper is ok for publication but I think this work does not meet the criteria of SciPost and I think can be better placed on JSTAT or PRD.

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

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