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On holographic entanglement density

On holographic entanglement density
On holographic entanglement density
We use holographic duality to study the entanglement entropy (EE) of Conformal Field Theories (CFTs) in various spacetime dimensions d, in the presence of various deformations: a relevant Lorentz scalar operator with constant source, a temperature T , a chemical potential μ, a marginal Lorentz scalar operator with source linear in a spatial coordinate, and a circle-compactified spatial direction. We consider EE between a strip or sphere sub-region and the rest of the system, and define the “entanglement density” (ED) as the change in EE due to the deformation, divided by the sub-region’s volume. Using the deformed CFTs above, we show how the ED’s dependence on the strip width or sphere radius, L, is useful for characterizing states of matter. For example, the ED’s small-L behavior is determined either by the dimension of the perturbing operator or by the first law of EE. For Lorentz-invariant renormalization group (RG) flows between CFTs, the “area theorem” states that the coefficient of the EE’s area law term must be larger in the UV than in the IR. In these cases the ED must therefore approach zero from below as L→∞. However, when Lorentz symmetry is broken and the IR fixed point has different scaling from the UV, we find that the ED often approaches the thermal entropy density from above, indicating area theorem violation.
1029-8479
Gushterov, Nikola I.
dc0f41ee-66a0-4e9f-91e4-f623515b96d2
O'Bannon, Andrew
f0c14b6c-5b74-4319-8432-f9eba1e20cf3
Rodgers, Ronald
50624100-db56-478e-9b46-0db869df1020
Gushterov, Nikola I.
dc0f41ee-66a0-4e9f-91e4-f623515b96d2
O'Bannon, Andrew
f0c14b6c-5b74-4319-8432-f9eba1e20cf3
Rodgers, Ronald
50624100-db56-478e-9b46-0db869df1020

Gushterov, Nikola I., O'Bannon, Andrew and Rodgers, Ronald (2017) On holographic entanglement density. Journal of High Energy Physics, 2017 (10), [137]. (doi:10.1007/JHEP10(2017)137).

Record type: Article

Abstract

We use holographic duality to study the entanglement entropy (EE) of Conformal Field Theories (CFTs) in various spacetime dimensions d, in the presence of various deformations: a relevant Lorentz scalar operator with constant source, a temperature T , a chemical potential μ, a marginal Lorentz scalar operator with source linear in a spatial coordinate, and a circle-compactified spatial direction. We consider EE between a strip or sphere sub-region and the rest of the system, and define the “entanglement density” (ED) as the change in EE due to the deformation, divided by the sub-region’s volume. Using the deformed CFTs above, we show how the ED’s dependence on the strip width or sphere radius, L, is useful for characterizing states of matter. For example, the ED’s small-L behavior is determined either by the dimension of the perturbing operator or by the first law of EE. For Lorentz-invariant renormalization group (RG) flows between CFTs, the “area theorem” states that the coefficient of the EE’s area law term must be larger in the UV than in the IR. In these cases the ED must therefore approach zero from below as L→∞. However, when Lorentz symmetry is broken and the IR fixed point has different scaling from the UV, we find that the ED often approaches the thermal entropy density from above, indicating area theorem violation.

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JHEP10(2017)137 - Version of Record
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Accepted/In Press date: 10 October 2017
e-pub ahead of print date: 20 October 2017

Identifiers

Local EPrints ID: 418600
URI: http://eprints.soton.ac.uk/id/eprint/418600
ISSN: 1029-8479
PURE UUID: f10742ec-3945-4b15-b60b-548c73f4547d
ORCID for Andrew O'Bannon: ORCID iD orcid.org/0000-0001-7862-783X
ORCID for Ronald Rodgers: ORCID iD orcid.org/0000-0002-4826-6540

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Date deposited: 12 Mar 2018 17:30
Last modified: 22 Nov 2021 03:09

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Contributors

Author: Nikola I. Gushterov
Author: Andrew O'Bannon ORCID iD
Author: Ronald Rodgers ORCID iD

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