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Consistency conditions for an AdS multiscale entanglement renormalization ansatz correspondence

Bao, Ning and Cao, ChunJun and Carroll, Sean M. and Chatwin-Davies, Aidan and Hunter-Jones, Nicholas and Pollack, Jason and Remmen, Grant N. (2015) Consistency conditions for an AdS multiscale entanglement renormalization ansatz correspondence. Physical Review D, 91 (12). Art. No. 125036. ISSN 1550-7998. doi:10.1103/PhysRevD.91.125036.

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The multiscale entanglement renormalization ansatz (MERA) is a tensor network that provides an efficient way of variationally estimating the ground state of a critical quantum system. The network geometry resembles a discretization of spatial slices of an anti–de Sitter (AdS) spacetime and “geodesics” in the MERA reproduce the Ryu-Takayanagi formula for the entanglement entropy of a boundary region in terms of bulk properties. It has therefore been suggested that there could be an AdS/MERA correspondence, relating states in the Hilbert space of the boundary quantum system to ones defined on the bulk lattice. Here we investigate this proposal and derive necessary conditions for it to apply, using geometric features and entropy inequalities that we expect to hold in the bulk. We show that, perhaps unsurprisingly, the MERA lattice can only describe physics on length scales larger than the AdS radius. Further, using the covariant entropy bound in the bulk, we show that there are no conventional MERA parameters that completely reproduce bulk physics even on super-AdS scales. We suggest modifications or generalizations of this kind of tensor network that may be able to provide a more robust correspondence.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper DOIArticle
Bao, Ning0000-0002-3296-1039
Cao, ChunJun0000-0002-5761-5474
Carroll, Sean M.0000-0002-4226-5758
Chatwin-Davies, Aidan0000-0003-1406-9271
Pollack, Jason0000-0003-4754-4905
Remmen, Grant N.0000-0001-6569-8866
Alternate Title:Consistency Conditions for an AdS/MERA Correspondence
Additional Information:© 2015 American Physical Society. Received 6 May 2015; published 29 June 2015. We thank Bartek Czech, Glen Evenbly, Daniel Harlow, Shamit Kachru, Shaun Maguire, Spiros Michalakis, Aleksander Kubica, Don Page, John Preskill, Bogdan Stoica, James Sully, Brian Swingle, and Guifré Vidal for helpful discussions. This research was supported in part by DOE Grant No. DE-SC0011632 and by the Gordon and Betty Moore Foundation through Grant No. 776 to the Caltech Moore Center for Theoretical Cosmology and Physics. N. B. is supported by the DuBridge postdoctoral fellowship at the Walter Burke Institute for Theoretical Physics. A. C.-D. and C. C. are supported by the NSERC Postgraduate Scholarship program. G. N. R. is supported by a Hertz Graduate Fellowship and a NSF Graduate Research Fellowship under Grant No. DGE-1144469.
Group:Walter Burke Institute for Theoretical Physics, Moore Center for Theoretical Cosmology and Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Gordon and Betty Moore Foundation776
DuBridge Postdoctoral FellowshipUNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Fannie and John Hertz FoundationUNSPECIFIED
NSF Graduate Research FellowshipDGE-1144469
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Other Numbering System NameOther Numbering System ID
Issue or Number:12
Classification Code:PACS: 03.65.Ud, 04.60.-m, 11.25.Hf,
Record Number:CaltechAUTHORS:20150601-131525807
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:57920
Deposited By: Joy Painter
Deposited On:01 Jun 2015 21:36
Last Modified:10 Nov 2021 21:56

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