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Flat entanglement spectra in fixed-area states of quantum gravity
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Journal Article
Flat entanglement spectra in fixed-area states of quantum gravity
2019
Overview
A
bstract
We use the Einstein-Hilbert gravitational path integral to investigate gravita- tional entanglement at leading order
O
(1
/G
). We argue that semiclassical states prepared by a Euclidean path integral have the property that projecting them onto a subspace in which the Ryu-Takayanagi or Hubeny-Rangamani-Takayanagi surface has definite area gives a state with a flat entanglement spectrum at this order in gravitational perturbation theory. This means that the reduced density matrix can be approximated as proportional to the identity to the extent that its Renyi entropies
Sn
are independent of
n
at this order. The
n
-dependence of
Sn
in more general states then arises from sums over the RT/HRT- area, which are generally dominated by different values of this area for each
n
. This provides a simple picture of gravitational entanglement, bolsters the connection between holographic systems and tensor network models, clarifies the bulk interpretation of alge- braic centers which arise in the quantum error-correcting description of holography, and strengthens the connection between bulk and boundary modular Hamiltonians described by Jafferis, Lewkowycz, Maldacena, and Suh.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V,Springer Berlin,SpringerOpen
