Boundary theories of critical matchgate tensor networks
Abstract 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 t...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-04-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP04(2022)111 |
| _version_ | 1797865804974260224 |
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| author | A. Jahn M. Gluza C. Verhoeven S. Singh J. Eisert |
| author_facet | A. Jahn M. Gluza C. Verhoeven S. Singh J. Eisert |
| author_sort | A. Jahn |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-04-09T23:14:37Z |
| format | Article |
| id | doaj.art-df45b139df5f460bb271ffffab9a71a2 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T23:14:37Z |
| publishDate | 2022-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-df45b139df5f460bb271ffffab9a71a22023-03-22T10:11:33ZengSpringerOpenJournal of High Energy Physics1029-84792022-04-012022414910.1007/JHEP04(2022)111Boundary theories of critical matchgate tensor networksA. Jahn0M. Gluza1C. Verhoeven2S. Singh3J. Eisert4Institute for Quantum Information and Matter, CaltechDahlem Center for Complex Quantum Systems, Freie Universität BerlinDahlem Center for Complex Quantum Systems, Freie Universität BerlinMax-Planck Institute for Gravitational Physics (Albert Einstein Institute)Dahlem Center for Complex Quantum Systems, Freie Universität BerlinAbstract 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.https://doi.org/10.1007/JHEP04(2022)111AdS-CFT CorrespondenceConformal Field Theory |
| spellingShingle | A. Jahn M. Gluza C. Verhoeven S. Singh J. Eisert Boundary theories of critical matchgate tensor networks Journal of High Energy Physics AdS-CFT Correspondence Conformal Field Theory |
| title | Boundary theories of critical matchgate tensor networks |
| title_full | Boundary theories of critical matchgate tensor networks |
| title_fullStr | Boundary theories of critical matchgate tensor networks |
| title_full_unstemmed | Boundary theories of critical matchgate tensor networks |
| title_short | Boundary theories of critical matchgate tensor networks |
| title_sort | boundary theories of critical matchgate tensor networks |
| topic | AdS-CFT Correspondence Conformal Field Theory |
| url | https://doi.org/10.1007/JHEP04(2022)111 |
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