Flat entanglement spectra in fixed-area states of quantum gravity

• Published in: The journal of high energy physics Vol. 2019; no. 10; pp. 1 - 25
• Main Authors: Dong, Xi, Harlow, Daniel, Marolf, Donald
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2019; Springer Nature B.V; Springer Berlin; SpringerOpen
• Subjects: AdS-CFT Correspondence; Classical and Quantum Gravitation; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Classical Theories of Gravity; Codes; Dependence; Elementary Particles; Error correction; Error correction & detection; Gauge-gravity correspondence; Geometry; Gravitation theory; Gravity; High energy physics; Holography; Integrals; Perturbation theory; Physics; Physics and Astronomy; Quantum entanglement; Quantum Field Theories; Quantum Field Theory; Quantum gravity; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Tensors; AdS-CFT Correspondence; Gauge-gravity correspondence; Classical Theories of Gravity
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP10(2019)240

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.