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Entanglement entropy from entanglement contour: higher dimensions

by Muxin Han, Qiang Wen

Submission summary

As Contributors: Qiang Wen
Preprint link: scipost_202111_00034v1
Date submitted: 2021-11-18 13:55
Submitted by: Wen, Qiang
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Gravitation, Cosmology and Astroparticle Physics
  • High-Energy Physics - Theory
  • Quantum Physics
Approach: Theoretical

Abstract

We study the \textit{entanglement contour} and \textit{partial entanglement entropy} (PEE) in quantum field theories in 3 and higher dimensions. The entanglement entropy can be evaluated from 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 general-dimensional CFTs.

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Submission scipost_202111_00034v1 on 18 November 2021

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