Boundary theories of critical matchgate tensor networks
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 transl...
| Main Authors: | , , , , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
2022
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| Online Access: | https://hdl.handle.net/10356/161288 |
| _version_ | 1824454801070489600 |
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| author | Jahn, Alexander Gluza, Marek Verhoeven, Charlotte Singh, Sukhbinder Eisert, Jens |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Jahn, Alexander Gluza, Marek Verhoeven, Charlotte Singh, Sukhbinder Eisert, Jens |
| author_sort | Jahn, Alexander |
| collection | NTU |
| description | 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 | 2025-02-19T03:28:05Z |
| format | Journal Article |
| id | ntu-10356/161288 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:28:05Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1612882023-02-28T20:11:49Z Boundary theories of critical matchgate tensor networks Jahn, Alexander Gluza, Marek Verhoeven, Charlotte Singh, Sukhbinder Eisert, Jens School of Physical and Mathematical Sciences Science::Physics AdS-CFT Correspondence Conformal Field Theory 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. Published version 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. 2022-08-24T01:22:41Z 2022-08-24T01:22:41Z 2022 Journal Article Jahn, A., Gluza, M., Verhoeven, C., Singh, S. & Eisert, J. (2022). Boundary theories of critical matchgate tensor networks. Journal of High Energy Physics, 2022(4). https://dx.doi.org/10.1007/JHEP04(2022)111 1126-6708 https://hdl.handle.net/10356/161288 10.1007/JHEP04(2022)111 2-s2.0-85128786883 4 2022 en Journal of High Energy Physics © 2022 The Authors. Article funded by SCOAP³.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. application/pdf |
| spellingShingle | Science::Physics AdS-CFT Correspondence Conformal Field Theory Jahn, Alexander Gluza, Marek Verhoeven, Charlotte Singh, Sukhbinder Eisert, Jens Boundary theories of critical matchgate tensor networks |
| 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 | Science::Physics AdS-CFT Correspondence Conformal Field Theory |
| url | https://hdl.handle.net/10356/161288 |
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