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Tensor network models of AdS/qCFT

Jahn, Alexander and Zimborás, Zoltán and Eisert, Jens (2022) Tensor network models of AdS/qCFT. Quantum, 6 . Art. No. 643. ISSN 2521-327X. doi:10.22331/q-2022-02-03-643.

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The study of critical quantum many-body systems through conformal field theory (CFT) is one of the pillars of modern quantum physics. Certain CFTs are also understood to be dual to higher-dimensional theories of gravity via the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. To reproduce various features of AdS/CFT, a large number of discrete models based on tensor networks have been proposed. Some recent models, most notably including toy models of holographic quantum error correction, are constructed on regular time-slice discretizations of AdS. In this work, we show that the symmetries of these models are well suited for approximating CFT states, as their geometry enforces a discrete subgroup of conformal symmetries. Based on these symmetries, we introduce the notion of a quasiperiodic conformal field theory (qCFT), a critical theory less restrictive than a full CFT and with characteristic multi-scale quasiperiodicity. We discuss holographic code states and their renormalization group flow as specific implementations of a qCFT with fractional central charges and argue that their behavior generalizes to a large class of existing and future models. Beyond approximating CFT properties, we show that these can be best understood as belonging to a paradigm of discrete holography.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Jahn, Alexander0000-0002-7142-0059
Zimborás, Zoltán0000-0002-2184-526X
Eisert, Jens0000-0003-3033-1292
Additional Information:© 2022 The Author(s). This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. Published: 2022-02-03. We thank Marek Gluza, Xiaoliang Qi, Sukhbinder Singh, Tadashi Takayanagi, and Charlotte Verhoeven for helpful comments and discussions. This work has been supported by the Simons Collaboration on It from Qubit, the Templeton Foundation, the DFG (CRC 183, EI 519/15-1), and the FQXi. This work has also received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 817482 (PASQuanS). This research has been supported in part 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 and Innovation. We also acknowledge support from the National Research, Development and Innovation Office (NKFIH) through the Quantum Information National Laboratory of Hungary and Grants No. K124176, FK135220, K124351.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Simons FoundationUNSPECIFIED
John Templeton FoundationUNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG)CRC 183
Deutsche Forschungsgemeinschaft (DFG)EI 519/15-1
Foundational Questions Institute (FQXI)UNSPECIFIED
European Research Council (ERC)817482
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
Department of Innovation, Science and Economic Development (Canada)UNSPECIFIED
Ontario Ministry of Research and InnovationUNSPECIFIED
National Research, Development and Innovation Office (Hungary)K124176
National Research, Development and Innovation Office (Hungary)FK135220
National Research, Development and Innovation Office (Hungary)K124351
Record Number:CaltechAUTHORS:20220414-470744800
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:114332
Deposited By: Tony Diaz
Deposited On:14 Apr 2022 19:17
Last Modified:14 Apr 2022 19:17

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