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Holographic duality between local Hamiltonians from random tensor networks

Journal of High Energy Physics volume 2022, Article number: 52 (2022) Cite this article

A preprint version of the article is available at arXiv.

Abstract

The AdS/CFT correspondence realises the holographic principle where information in the bulk of a space is encoded at its border. We are yet a long way from a full mathematical construction of AdS/CFT, but toy models in the form of holographic quantum error correcting codes (HQECC) have replicated some interesting features of the correspondence. In this work we construct new HQECCs built from random stabilizer tensors that describe a duality between models encompassing local Hamiltonians whilst exactly obeying the Ryu-Takayanagi entropy formula for all boundary regions. We also obtain complementary recovery of local bulk operators for any boundary bipartition. Existing HQECCs have been shown to exhibit these properties individually, whereas our mathematically rigorous toy models capture these features of AdS/CFT simultaneously, advancing further towards a complete construction of holographic duality.

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Authors and Affiliations

  1. Department of Computer Science, University College London, Gower St., London, WC1E 6EA, UK

    Harriet Apel, Tamara Kohler & Toby Cubitt

Authors
  1. Harriet Apel
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  2. Tamara Kohler
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  3. Toby Cubitt
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Correspondence to Harriet Apel.

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ArXiv ePrint: 2105.12067

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Apel, H., Kohler, T. & Cubitt, T. Holographic duality between local Hamiltonians from random tensor networks. J. High Energ. Phys. 2022, 52 (2022). https://doi.org/10.1007/JHEP03(2022)052

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  • DOI: https://doi.org/10.1007/JHEP03(2022)052

Keywords

  • AdS-CFT Correspondence
  • Gauge-Gravity Correspondence
  • Models of Quantum Gravity
  • Random Systems