Some results on the shape dependence of entanglement and Renyi entropies
Name
PhysRevD.91.046002.pdf
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1.1 MB
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Author(s)
Allais, Andrea
Mezei, Mark Koppany
Date Issued
February 2015
Journal
Physical Review D
Publisher
American Physical Society
Citation
Allais, Andrea, and Mark Mezei. "Some results on the shape dependence of entanglement and Renyi entropies." Phys. Rev. D 91, 046002 (February 2015). © 2015 American Physical Society
Version
Final published version
Abstract
We study how the universal contribution to entanglement entropy in a conformal field theory depends on the entangling region. We show that for a deformed sphere the variation of the universal contribution is quadratic in the deformation amplitude. We generalize these results for Renyi entropies. We obtain an explicit expression for the second order variation of entanglement entropy in the case of a deformed circle in a three-dimensional conformal field theory with a gravity dual. For the same system, we also consider an elliptic entangling region and determine numerically the entanglement entropy as a function of the aspect ratio of the ellipse. Based on these three-dimensional results and Solodukhin’s formula in four dimensions, we conjecture that the sphere minimizes the universal contribution to entanglement entropy in all dimensions.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevD.91.046002
