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Title: Boundary theories of critical matchgate tensor networks
Authors: Jahn, Alexander
Gluza, Marek
Verhoeven, Charlotte
Singh, Sukhbinder
Eisert, Jens
Keywords: Science::Physics
Issue Date: 2022
Source: 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).
Journal: Journal of High Energy Physics
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.
ISSN: 1126-6708
DOI: 10.1007/JHEP04(2022)111
Schools: School of Physical and Mathematical Sciences 
Rights: © 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.
Fulltext Permission: open
Fulltext Availability: With Fulltext
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