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Nonarchimedean Holographic Entropy from Networks of Perfect Tensors

Heydeman, Matthew and Marcolli, Matilde and Parikh, Sarthak and Saberi, Ingmar (2018) Nonarchimedean Holographic Entropy from Networks of Perfect Tensors. . (Submitted)

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We consider a class of holographic quantum error-correcting codes, built from perfect tensors in network configurations dual to Bruhat-Tits trees and their quotients by Schottky groups corresponding to BTZ black holes. The resulting holographic states can be constructed in the limit of infinite network size. We obtain a p-adic version of entropy which obeys a Ryu-Takayanagi like formula for bipartite entanglement of connected or disconnected regions, in both genus-zero and genus-one p-adic backgrounds, along with a Bekenstein-Hawking-type formula for black hole entropy. We prove entropy inequalities obeyed by such tensor networks, such as subadditivity, strong subadditivity, and monogamy of mutual information (which is always saturated). In addition, we construct infinite classes of perfect tensors directly from semiclassical states in phase spaces over finite fields, generalizing the CRSS algorithm, and give Hamiltonians exhibiting these as vacua.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:I.A.S. thanks D. Aasen, J. Keating, and J. Walcher for conversations, and the Kavli Institute for Theoretical Physics in Santa Barbara for hospitality as this manuscript was being completed; he also gratefully acknowledges partial support by the Deutsche Forschungsgemeinschaft, within the framework of the Exzellenzinitiative an der Universität Heidelberg. M.H. and S.P. thank Perimeter Institute for their kind hospitality while this work was in its early stages. The work of M.H. and S.P. was supported in part by Perimeter Institute for Theoretical Physics. M.H. would like to thank S.S. Gubser and Princeton University for their hospitality while this work was being completed, and work done at Princeton was supported in part by the Department of Energy under Grant No. DE-FG02-91ER40671, and by the Simons Foundation, Grant 511167 (SSG). M.H. is also partially supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number de-sc0011632. M.M. is partially supported by NSF grant DMS-1707882, by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement grant RGPAS-2018-522593, and by the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Research, Innovation and Science. Research at the Kavli Institute is supported in part by the National Science Foundation under Grant No. PHY-1748958
Group:Walter Burke Institute for Theoretical Physics
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Deutsche Forschungsgemeinschaft (DFG)UNSPECIFIED
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
Department of Energy (DOE)DE-FG02-91ER40671
Simons Foundation511167
Department of Energy (DOE)DE-SC0011632
Natural Sciences and Engineering Research Council of Canada (NSERC)RGPIN-2018-04937
Natural Sciences and Engineering Research Council of Canada (NSERC)RGPAS-2018-522593
Ontario Ministry of Research and InnovationUNSPECIFIED
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Record Number:CaltechAUTHORS:20190115-160601117
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92302
Deposited By: Joy Painter
Deposited On:16 Jan 2019 00:26
Last Modified:16 Jan 2019 19:47

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