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The infinite-dimensional HaPPY code: entanglement wedge reconstruction and dynamics

Gesteau, Elliott and Kang, Monica Jinwoo (2020) The infinite-dimensional HaPPY code: entanglement wedge reconstruction and dynamics. . (Submitted)

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We construct an infinite-dimensional analog of the HaPPY code as a growing series of stabilizer codes defined respective to their Hilbert spaces. The Hilbert spaces are related by isometric maps, which we define explicitly. We construct a Hamiltonian that is compatible with the infinite-dimensional HaPPY code and further study the stabilizer of our code, which has an inherent fractal structure. We use this result to study the dynamics of the code and map a nontrivial bulk Hamiltonian to the boundary. We find that the image of the mapping is scale invariant, but does not create any long-range entanglement in the boundary, therefore failing to reproduce the features of a CFT. This result shows the limits of the HaPPY code as a model of the AdS/CFT correspondence, but also hints that the relevance of quantum error correction in quantum gravity may not be limited to the CFT context.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:The authors are grateful to Vincent Chen, Adrian Franco-Rubio, David Kolchmeyer, and Matilde Marcolli for discussions and Craig Lawrie for helpful comments on this paper. M.J.K. is supported by a Sherman Fairchild Postdoctoral Fellowship. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. E.G. is funded by ENS Paris and would like to thank Matilde Marcolli for her guidance and constant support. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities.
Group:Walter Burke Institute for Theoretical Physics
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Department of Energy (DOE)DE-SC0011632
Innovation, Science and Economic Development CanadaUNSPECIFIED
Ontario Ministry of Colleges and UniversitiesUNSPECIFIED
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Record Number:CaltechAUTHORS:20200521-140047377
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103381
Deposited By: Joy Painter
Deposited On:21 May 2020 21:21
Last Modified:21 May 2020 21:21

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