Apel, Harriet;
Kohler, Tamara;
Cubitt, Toby;
(2022)
Holographic duality between local Hamiltonians from random tensor networks.
Journal of High Energy Physics
, 2022
(3)
, Article 052. 10.1007/JHEP03(2022)052.
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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.
| Type: | Article |
|---|---|
| Title: | Holographic duality between local Hamiltonians from random tensor networks |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/JHEP03(2022)052 |
| Publisher version: | https://doi.org/10.1007/JHEP03(2022)052 |
| Language: | English |
| Additional information: | This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. |
| Keywords: | AdS-CFT Correspondence; Gauge-Gravity Correspondence; Models of Quantum Gravity; Random Systems |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10146042 |
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