Large-d phase transitions in holographic mutual information
Abstract
In the AdS/CFT correspondence, the entanglement entropy of subregions in the boundary CFT is conjectured to be dual to the area of a bulk extremal surface at leading order in GN in the holographic limit. Under this dictionary, distantly separated regions in the CFT vacuum state have zero mutual information at leading order, and only attain nonzero mutual information at this order when they lie close enough to develop significant classical and quantum correlations. Previously, the separation at which this phase transition occurs for equal-size ball-shaped regions centered at antipodal points on the boundary was known analytically only in 3 spacetime dimensions. Inspired by recent explorations of general relativity at large-d, we compute the separation at which the phase transition occurs analytically in the limit of infinitely many spacetime dimensions, and find that distant regions cannot develop large correlations without collectively occupying the entire volume of the boundary theory. We interpret this result as illustrating the spatial decoupling of holographic correlations in the large-d limit, and provide intuition for this phenomenon using results from quantum information theory. We also compute the phase transition separation numerically for a range of bulk spacetime dimensions from 4 to 21, where analytic results aremore »
- Authors:
-
- Univ. of California, Davis, CA (United States)
- Katholieke Univ. Leuven (Belgium)
- Stanford Univ., CA (United States)
- Publication Date:
- Research Org.:
- Univ. of California, Davis, CA (United States)
- Sponsoring Org.:
- USDOE; European Union's Horizon 2020; European Research Council (ERC); US Air Force Office of Scientific Research (AFOSR); Qubit Collaboration
- OSTI Identifier:
- 1659667
- Grant/Contract Number:
- SC0009999; 665501; ERC-2013-CoG 61673 HoloQosmos; SC0019380
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 4; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Gauge-gravity correspondence
Citation Formats
Colin-Ellerin, Sean, Hubeny, Veronika E., Niehoff, Benjamin E., and Sorce, Jonathan. Large-d phase transitions in holographic mutual information. United States: N. p., 2020.
Web. doi:10.1007/jhep04(2020)173.
Colin-Ellerin, Sean, Hubeny, Veronika E., Niehoff, Benjamin E., & Sorce, Jonathan. Large-d phase transitions in holographic mutual information. United States. https://doi.org/10.1007/jhep04(2020)173
Colin-Ellerin, Sean, Hubeny, Veronika E., Niehoff, Benjamin E., and Sorce, Jonathan. Mon .
"Large-d phase transitions in holographic mutual information". United States. https://doi.org/10.1007/jhep04(2020)173. https://www.osti.gov/servlets/purl/1659667.
@article{osti_1659667,
title = {Large-d phase transitions in holographic mutual information},
author = {Colin-Ellerin, Sean and Hubeny, Veronika E. and Niehoff, Benjamin E. and Sorce, Jonathan},
abstractNote = {In the AdS/CFT correspondence, the entanglement entropy of subregions in the boundary CFT is conjectured to be dual to the area of a bulk extremal surface at leading order in GN in the holographic limit. Under this dictionary, distantly separated regions in the CFT vacuum state have zero mutual information at leading order, and only attain nonzero mutual information at this order when they lie close enough to develop significant classical and quantum correlations. Previously, the separation at which this phase transition occurs for equal-size ball-shaped regions centered at antipodal points on the boundary was known analytically only in 3 spacetime dimensions. Inspired by recent explorations of general relativity at large-d, we compute the separation at which the phase transition occurs analytically in the limit of infinitely many spacetime dimensions, and find that distant regions cannot develop large correlations without collectively occupying the entire volume of the boundary theory. We interpret this result as illustrating the spatial decoupling of holographic correlations in the large-d limit, and provide intuition for this phenomenon using results from quantum information theory. We also compute the phase transition separation numerically for a range of bulk spacetime dimensions from 4 to 21, where analytic results are intractable but numerical results provide insight into the dimension-dependence of holographic correlations. For bulk dimensions above 5, our exact numerical results are well approximated analytically by working to next-to-leading order in the large-d expansion.},
doi = {10.1007/jhep04(2020)173},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2020,
place = {United States},
year = {Mon Apr 27 00:00:00 EDT 2020},
month = {Mon Apr 27 00:00:00 EDT 2020}
}
Web of Science
Works referenced in this record:
Causality & holographic entanglement entropy
journal, December 2014
- Headrick, Matthew; Hubeny, Veronika E.; Lawrence, Albion
- Journal of High Energy Physics, Vol. 2014, Issue 12
The gravity dual of a density matrix
journal, July 2012
- Czech, Bartłomiej; Karczmarek, Joanna L.; Nogueira, Fernando
- Classical and Quantum Gravity, Vol. 29, Issue 15
The connection between holographic entanglement and complexity of purification
journal, September 2019
- Ghodrati, Mahdis; Kuang, Xiao-Mei; Wang, Bin
- Journal of High Energy Physics, Vol. 2019, Issue 9
Locally normal symmetric states and an analogue of de Finetti's theorem
journal, December 1976
- Hudson, R. L.; Moody, G. R.
- Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 33, Issue 4
Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy
journal, November 2014
- Wall, Aron C.
- Classical and Quantum Gravity, Vol. 31, Issue 22
A covariant holographic entanglement entropy proposal
journal, July 2007
- Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi
- Journal of High Energy Physics, Vol. 2007, Issue 07
Universal thermal corrections to entanglement entropy for conformal field theories on spheres
journal, October 2014
- Herzog, Christopher P.
- Journal of High Energy Physics, Vol. 2014, Issue 10
The Holographic Entropy Arrangement
journal, February 2019
- Hubeny, Veronika E.; Rangamani, Mukund; Rota, Massimiliano
- Fortschritte der Physik, Vol. 67, Issue 4
A quasipolynomial-time algorithm for the quantum separability problem
conference, January 2011
- Brandão, Fernando G. S. L.; Christandl, Matthias; Yard, Jon
- Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11
The large D limit of General Relativity
journal, June 2013
- Emparan, Roberto; Suzuki, Ryotaku; Tanabe, Kentaro
- Journal of High Energy Physics, Vol. 2013, Issue 6
Aspects of holographic entanglement entropy
journal, August 2006
- Ryu, Shinsei; Takayanagi, Tadashi
- Journal of High Energy Physics, Vol. 2006, Issue 08
Holographic entanglement entropy: near horizon geometry and disconnected regions
journal, May 2011
- Tonni, Erik
- Journal of High Energy Physics, Vol. 2011, Issue 5
Aspects of holographic entanglement at finite temperature and chemical potential
journal, August 2016
- Kundu, Sandipan; Pedraza, Juan F.
- Journal of High Energy Physics, Vol. 2016, Issue 8
Symmetric states of infinite tensor products of C∗-algebras
journal, February 1969
- Størmer, Erling
- Journal of Functional Analysis, Vol. 3, Issue 1
Deriving covariant holographic entanglement
journal, November 2016
- Dong, Xi; Lewkowycz, Aitor; Rangamani, Mukund
- Journal of High Energy Physics, Vol. 2016, Issue 11
Holographic entanglement entropy is cutoff-covariant
journal, October 2019
- Sorce, Jonathan
- Journal of High Energy Physics, Vol. 2019, Issue 10
Holographic Entropy Relations
journal, September 2018
- Hubeny, Veronika E.; Rangamani, Mukund; Rota, Massimiliano
- Fortschritte der Physik, Vol. 66, Issue 11-12
Black holes and the butterfly effect
journal, March 2014
- Shenker, Stephen H.; Stanford, Douglas
- Journal of High Energy Physics, Vol. 2014, Issue 3
Conformal blocks in the large D limit
journal, August 2013
- Fitzpatrick, A. Liam; Kaplan, Jared; Poland, David
- Journal of High Energy Physics, Vol. 2013, Issue 8
The holographic entropy cone
journal, September 2015
- Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi
- Journal of High Energy Physics, Vol. 2015, Issue 9
Symmetric states of infinite tensor products of C∗-algebras
journal, February 1969
- Størmer, Erling
- Journal of Functional Analysis, Vol. 3, Issue 1
Some results on the mutual information of disjoint regions in higher dimensions
journal, June 2013
- Cardy, John
- Journal of Physics A: Mathematical and Theoretical, Vol. 46, Issue 28
Monogamy of entanglement and improved mean-field ansatz for spin lattices
journal, March 2015
- Osterloh, Andreas; Schützhold, Ralf
- Physical Review B, Vol. 91, Issue 12
Quantum corrections to holographic entanglement entropy
text, January 2013
- Faulkner, Thomas; Lewkowycz, Aitor; Maldacena, Juan
- arXiv
Gravitation from Entanglement in Holographic CFTs
text, January 2013
- Faulkner, Thomas; Guica, Monica; Hartman, Thomas
- arXiv
Minimal surfaces and entanglement entropy in anti-de Sitter space
text, January 2014
- Krtous, Pavel; Zelnikov, Andrei
- arXiv
The holographic entropy arrangement
text, January 2018
- Hubeny, Veronika E.; Rangamani, Mukund; Rota, Massimiliano
- arXiv
Quantum statistical mechanics of general mean field systems
text, January 1989
- G. A., Raggio,; R. F., Werner,
- Birkhäuser