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A first law of entanglement rates from holography

A first law of entanglement rates from holography
A first law of entanglement rates from holography
For a perturbation of the state of a conformal field theory (CFT), the response of the entanglement entropy is governed by the so-called “first law” of entanglement entropy, in which the change in entanglement entropy is proportional to the change in energy. Whether such a first law holds for other types of perturbations, such as a change to the CFT Lagrangian, remains an open question. We use holography to study the evolution in time t of entanglement entropy for a CFT driven by a t-linear source for a conserved U(1) current or marginal scalar operator. We find that although the usual first law of entanglement entropy may be violated, a first law for the rates of change of entanglement entropy and energy still holds. More generally, we prove that this first law for rates holds in holography for any asymptotically (d+1)-dimensional anti–de Sitter metric perturbation whose t dependence first appears at order zd in the Fefferman-Graham expansion about the boundary at z=0.
2470-0010
O'Bannon, Andrew
f0c14b6c-5b74-4319-8432-f9eba1e20cf3
Probst, Jonas
79a41e05-0c37-4efd-844d-cda7815aa622
Rodgers, Ronald, James
50624100-db56-478e-9b46-0db869df1020
Uhlemann, Christoph F.
a364423d-b17f-497f-9d3f-aca80883640c
O'Bannon, Andrew
f0c14b6c-5b74-4319-8432-f9eba1e20cf3
Probst, Jonas
79a41e05-0c37-4efd-844d-cda7815aa622
Rodgers, Ronald, James
50624100-db56-478e-9b46-0db869df1020
Uhlemann, Christoph F.
a364423d-b17f-497f-9d3f-aca80883640c

O'Bannon, Andrew, Probst, Jonas, Rodgers, Ronald, James and Uhlemann, Christoph F. (2017) A first law of entanglement rates from holography. Physical Review D, 96, [066028]. (doi:10.1103/PhysRevD.96.066028).

Record type: Article

Abstract

For a perturbation of the state of a conformal field theory (CFT), the response of the entanglement entropy is governed by the so-called “first law” of entanglement entropy, in which the change in entanglement entropy is proportional to the change in energy. Whether such a first law holds for other types of perturbations, such as a change to the CFT Lagrangian, remains an open question. We use holography to study the evolution in time t of entanglement entropy for a CFT driven by a t-linear source for a conserved U(1) current or marginal scalar operator. We find that although the usual first law of entanglement entropy may be violated, a first law for the rates of change of entanglement entropy and energy still holds. More generally, we prove that this first law for rates holds in holography for any asymptotically (d+1)-dimensional anti–de Sitter metric perturbation whose t dependence first appears at order zd in the Fefferman-Graham expansion about the boundary at z=0.

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A First Law of Entanglement Rates from Holography - Accepted Manuscript
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Accepted/In Press date: 1 September 2017
e-pub ahead of print date: 21 September 2017

Identifiers

Local EPrints ID: 413790
URI: http://eprints.soton.ac.uk/id/eprint/413790
ISSN: 2470-0010
PURE UUID: 4ee50e8d-3903-4e7e-b688-fd11fdcd7238
ORCID for Andrew O'Bannon: ORCID iD orcid.org/0000-0001-7862-783X
ORCID for Ronald, James Rodgers: ORCID iD orcid.org/0000-0002-4826-6540

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Date deposited: 06 Sep 2017 16:31
Last modified: 22 Nov 2021 05:43

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Contributors

Author: Andrew O'Bannon ORCID iD
Author: Jonas Probst
Author: Ronald, James Rodgers ORCID iD
Author: Christoph F. Uhlemann

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