Klco, Natalie and Savage, Martin J.
(2021)
*Entanglement Spheres and a UV-IR connection in Effective Field Theories.*
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(Unpublished)
https://resolver.caltech.edu/CaltechAUTHORS:20210408-123011098

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## Abstract

Disjoint regions of the latticized, massless scalar field vacuum become separable at large distances beyond the entanglement sphere, a distance that extends to infinity in the continuum limit. Through numerical calculations in one-, two- and three-dimensions, the radius of an entanglement sphere is found to be determined by the highest momentum mode of the field supported across the diameter, d, of two identical regions. As a result, the long-distance behavior of the entanglement is determined by the short-distance structure of the field. Effective field theories (EFTs), describing a system up to a given momentum scale Λ, are expected to share this feature, with regions of the EFT vacuum separable (or dependent on the UV-completion) beyond a distance proportional to Λ. The smallest non-zero value of the entanglement negativity supported by the field at large distances is conjectured to be N_N/∼e^(−Λd), independent of the number of spatial dimensions. This phenomenon may be manifest in perturbative QCD processes.

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Additional Information: | Attribution 4.0 International (CC BY 4.0). We would like to thank Silas Beane, Douglas Beck, Roland Farrell, David Kaplan, Aidan Murran, John Preskill, and Alessandro Roggero for valuable discussions. We have made extensive use of Wolfram Mathematica [70] and the Avanpix multiprecision computing toolbox [71] for MATLAB [72]. Numerical results are available upon request. NK is supported in part by the Walter Burke Institute for Theoretical Physics, and by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, (DE-SC0020290), and Office of High Energy Physics DEACO2-07CH11359. MJS was supported in part by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, InQubator for Quantum Simulation (IQuS) under Award Number DOE (NP) Award DESC0020970. | ||||||||||

Group: | Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics | ||||||||||

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Record Number: | CaltechAUTHORS:20210408-123011098 | ||||||||||

Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20210408-123011098 | ||||||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||

ID Code: | 108660 | ||||||||||

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Deposited By: | Tony Diaz | ||||||||||

Deposited On: | 09 Apr 2021 18:04 | ||||||||||

Last Modified: | 09 Apr 2021 18:04 |

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