Surface growth scheme for bulk reconstruction and tensor network

TL;DR

This paper introduces a surface growth scheme for bulk spacetime reconstruction using tensor networks, demonstrating that MERA-like networks discretize AdS spacetime and extending the method for more general surface growth and entanglement wedge reconstruction.

Contribution

It presents a novel surface growth approach to bulk reconstruction, establishing a direct link between tensor networks and AdS spacetime, and generalizes the method for broader applications.

Findings

MERA-like tensor network is equivalent to a discretized AdS time slice.

Surface growth approach provides an intuitive framework for entanglement wedge reconstruction.

Generalized method extends the surface growth scheme to more complex geometries.

Abstract

We propose a surface growth approach to reconstruct the bulk spacetime geometry, motivated by Huygens'principle of wave propagation. We first construct a tensor network corresponding to a special surface growth picture with spherical symmetry and fractal feature using the one-shot entanglement distillation (OSED)method and show that the resulting tensor network is equivalent to the MERA-like tensor network, which gives a proof that the MERA-like tensor network is indeed a discretized version of the time slice of AdS spacetime, rather than just an analogy. Furthermore, we generalize the original OSED method to describe more general surface growth picture by using of surface/state correspondence and generalized RT formula, which leads to a more profound understanding for the surface growth process and provides a concrete and intuitive way for the idea of entanglement wedge reconstruction.