The Large $N$ Limit of icMERA and Holography

TL;DR

This paper computes entanglement entropy in continuous icMERA tensor networks for large N models at strong coupling, revealing connections between quantum corrections in tensor networks and holographic minimal surfaces, advancing the understanding of spacetime emergence.

Contribution

It presents the first tensor network calculations at large N and strong coupling, linking quantum corrections in tensor networks to holographic entanglement entropy.

Findings

Quantum corrections to Fisher information relate to minimal surface corrections.

Different non-Gaussian entanglers affect subleading entropy terms.

Large N entropy correlates with leading holographic area term.

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.