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The Large $N$ Limit of icMERA and Holography

by Jose J. Fernandez-Melgarejo, Javier Molina-Vilaplana

Submission summary

As Contributors: Javier Molina Vilaplana
Arxiv Link: https://arxiv.org/abs/2107.13248v2 (pdf)
Date submitted: 2021-09-22 09:30
Submitted by: Molina Vilaplana, Javier
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Gravitation, Cosmology and Astroparticle Physics
  • High-Energy Physics - Theory
  • Quantum Physics
Approach: Theoretical

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, can be related to quantum corrections to the minimal area surface in the 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 results thus very suggestive. These results, which to our knowledge suppose the first tensor network calculations at large $N$ and strong coupling, pave the road for using tensor networks to describe the emergence of continuous spacetime geometries from the the structure of entanglement in quantum field theory.

Current status:
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Submission 2107.13248v2 on 22 September 2021

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