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Boundary theories of critical matchgate tensor networks

Jahn, A. and Gluza, M. and Verhoeven, C. and Singh, S. and Eisert, J. (2022) Boundary theories of critical matchgate tensor networks. Journal of High Energy Physics, 2022 (4). Art. No. 111. ISSN 1029-8479. doi:10.1007/jhep04(2022)111.

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Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states whose site-averaged ground state properties match the translation-invariant critical Ising model. In this work, we substantially sharpen this relationship by deriving disordered local Hamiltonians generalizing the critical Ising model whose ground and low-energy excited states are accurately represented by the matchgate ansatz without any averaging. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model based on layers of the hyperbolic lattice, breaking the conformal symmetries of the critical Ising model in a controlled manner. We provide a direct identification of correlation functions of ground and low-energy excited states between the disordered and translation-invariant models and give numerical evidence that the former approaches the latter in the large bond dimension limit. This establishes tensor networks on regular hyperbolic tilings as an effective tool for the study of conformal field theories. Furthermore, our numerical probes of the bulk parameters corresponding to boundary excited states constitute a first step towards a tensor network bulk-boundary dictionary between regular hyperbolic geometries and critical boundary states.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Jahn, A.0000-0002-7142-0059
Gluza, M.0000-0003-2836-9523
Singh, S.0000-0002-3099-4179
Eisert, J.0000-0003-3033-1292
Additional Information:© 2022 The Authors. 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. Article funded by SCOAP3. Received: November 19, 2021; Accepted: March 24, 2022; Published: April 20, 2022. We thank the DFG (EI 519/15-1, CRC 183, projects B01 and A03) for support. A. J. has been supported by the FQXi and the Simons Collaboration on It from Qubit: Quantum Fields, Gravity, and Information. This work has also received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 817482 (PASQuanS). SS acknowledges the support provided by the Alexander von Humboldt Foundation and the Federal Ministry for Education and Research through the Sofja Kovalevskaja Award while he was employed at the Max-Planck Institute for Gravitational Physics in Potsdam.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)EI 519/15-1
Deutsche Forschungsgemeinschaft (DFG)CRC 183
Foundational Questions Institute (FQXI)UNSPECIFIED
Simons FoundationUNSPECIFIED
European Research Council (ERC)817482
Alexander von Humboldt FoundationUNSPECIFIED
Subject Keywords:AdS-CFT Correspondence; Conformal Field Theory
Issue or Number:4
Record Number:CaltechAUTHORS:20220603-310946700
Persistent URL:
Official Citation:Jahn, A., Gluza, M., Verhoeven, C. et al. Boundary theories of critical matchgate tensor networks. J. High Energ. Phys. 2022, 111 (2022).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115021
Deposited By: Tony Diaz
Deposited On:03 Jun 2022 23:56
Last Modified:03 Jun 2022 23:56

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