The Large $N$ Limit of icMERA and Holography

• URL: http://arxiv.org/abs/2107.13248v3
• Date: Wed, 6 Apr 2022 08:30:20 GMT
• Title: The Large $N$ Limit of icMERA and Holography
• Authors: Jose J. Fernandez-Melgarejo, Javier Molina-Vilaplana
• Abstract summary: We compute the entanglement entropy in continuous icMERA tensor networks for large $N$ models at strong coupling. Our results constitute the first tensor network calculations at large $N$ and strong coupling simultaneously.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we compute the entanglement entropy in continuous icMERA tensor networks for large $N$ models at strong coupling. Our results show that the $1/N$ quantum corrections to the Fisher information metric (interpreted as a local bond dimension of the tensor network) in an icMERA circuit, are related to quantum corrections to the minimal area surface in the Ryu-Takayanagi formula. Upon picking two different non-Gaussian entanglers to build the icMERA circuit, the results for the entanglement entropy only differ at subleading orders in $1/G_N$, i.e, at the structure of the quantum corrections in the bulk. The fact that the large $N$ part of the entropy can be always related to the leading area term of the holographic calculation is very suggestive. These results, constitute the first tensor network calculations at large $N$ and strong coupling simultaneously, pushing the field of tensor network descriptions of the emergence of dual spacetime geometries from the structure of entanglement in quantum field theory.

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