Flat entanglement spectra in fixed-area states of quantum gravity
Abstract 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-...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-10-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP10(2019)240 |
| _version_ | 1819171379831898112 |
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| author | Xi Dong Daniel Harlow Donald Marolf |
| author_facet | Xi Dong Daniel Harlow Donald Marolf |
| author_sort | Xi Dong |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-12-22T19:50:22Z |
| format | Article |
| id | doaj.art-37f01591b61e4077a75b96ae72da7912 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-22T19:50:22Z |
| publishDate | 2019-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-37f01591b61e4077a75b96ae72da79122022-12-21T18:14:34ZengSpringerOpenJournal of High Energy Physics1029-84792019-10-0120191012510.1007/JHEP10(2019)240Flat entanglement spectra in fixed-area states of quantum gravityXi Dong0Daniel Harlow1Donald Marolf2Department of Physics, University of CaliforniaCenter for Theoretical Physics, Massachusetts Institute of TechnologyDepartment of Physics, University of CaliforniaAbstract 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.http://link.springer.com/article/10.1007/JHEP10(2019)240AdS-CFT CorrespondenceGauge-gravity correspondenceClassical Theories of Gravity |
| spellingShingle | Xi Dong Daniel Harlow Donald Marolf Flat entanglement spectra in fixed-area states of quantum gravity Journal of High Energy Physics AdS-CFT Correspondence Gauge-gravity correspondence Classical Theories of Gravity |
| title | Flat entanglement spectra in fixed-area states of quantum gravity |
| title_full | Flat entanglement spectra in fixed-area states of quantum gravity |
| title_fullStr | Flat entanglement spectra in fixed-area states of quantum gravity |
| title_full_unstemmed | Flat entanglement spectra in fixed-area states of quantum gravity |
| title_short | Flat entanglement spectra in fixed-area states of quantum gravity |
| title_sort | flat entanglement spectra in fixed area states of quantum gravity |
| topic | AdS-CFT Correspondence Gauge-gravity correspondence Classical Theories of Gravity |
| url | http://link.springer.com/article/10.1007/JHEP10(2019)240 |
| work_keys_str_mv | AT xidong flatentanglementspectrainfixedareastatesofquantumgravity AT danielharlow flatentanglementspectrainfixedareastatesofquantumgravity AT donaldmarolf flatentanglementspectrainfixedareastatesofquantumgravity |