Hyper-invariant tensor networks and holography

TL;DR

This paper introduces hyper-invariant tensor networks as a new model for holography and AdS/CFT, capturing key features of entanglement and correlation while avoiding limitations of previous models like MERA.

Contribution

It presents a novel tensor network construction based on hyperbolic tiling that preserves holographic features without directional bias, advancing the modeling of AdS/CFT correspondence.

Findings

Retains algebraic correlation functions and efficient contractibility.

Establishes an equivalence between causal cones and entanglement wedges.

Circumvents key limitations of MERA in holographic modeling.

Abstract

We propose a new class of tensor network state as a model for the AdS/CFT correspondence and holography. This class is demonstrated to retain key features of the multi-scale entanglement renormalization ansatz (MERA), in that they describe quantum states with algebraic correlation functions, have free variational parameters, and are efficiently contractible. Yet, unlike MERA, they are built according to a uniform tiling of hyperbolic space, without inherent directionality or preferred locations in the holographic bulk, and thus circumvent key arguments made against the MERA as a model for AdS/CFT. Novel holographic features of this tensor network class are examined, such as an equivalence between the causal cones C(R) and the entanglement wedges E(R) of connected boundary regions R.