Constructing holographic spacetimes using entanglement renormalization

TL;DR

This paper explores how entanglement renormalization can naturally produce classical holographic spacetimes in the large N limit, linking tensor networks with emergent geometry and holographic duality.

Contribution

It demonstrates that features of holographic duality, including classical spacetime and phase transitions, emerge from entanglement renormalization in the large N limit.

Findings

Classical spacetime emerges from entanglement in the large N limit.

Features like sparse operator spectra and phase transitions are naturally explained.

Connections between quantum expanders and spacetime construction are proposed.

Abstract

We elaborate on our earlier proposal connecting entanglement renormalization and holographic duality in which we argued that a tensor network can be reinterpreted as a kind of skeleton for an emergent holographic space. Here we address the question of the large $N$ limit where on the holographic side the gravity theory becomes classical and a non-fluctuating smooth spacetime description emerges. We show how a number of features of holographic duality in the large $N$ limit emerge naturally from entanglement renormalization, including a classical spacetime generated by entanglement, a sparse spectrum of operator dimensions, and phase transitions in mutual information. We also address questions related to bulk locality below the AdS radius, holographic duals of weakly coupled large $N$ theories, Fermi surfaces in holography, and the holographic interpretation of branching MERA. Some of our considerations are inspired by the idea of quantum expanders which are generalized quantum transformations that add a definite amount of entropy to most states. Since we identify entanglement with geometry, we thus argue that classical spacetime may be built from quantum expanders (or something like them).