Holographic duality between local Hamiltonians from random tensor networks

TL;DR

This paper introduces new holographic quantum error correcting codes built from random stabilizer tensors that simultaneously encode local Hamiltonians and obey the Ryu-Takayanagi entropy formula, advancing towards a rigorous model of AdS/CFT.

Contribution

The authors construct mathematically rigorous HQECCs from random stabilizer tensors that capture multiple key features of holographic duality simultaneously.

Findings

Models obey the Ryu-Takayanagi entropy formula for all boundary regions.

Achieve complementary recovery of bulk operators for any boundary bipartition.

Capture features of AdS/CFT in a unified, rigorous toy model.

Abstract

The AdS/CFT correspondence realises the holographic principle where information in the bulk of a space is encoded at its border. We are yet a long way from a full mathematical construction of AdS/CFT, but toy models in the form of holographic quantum error correcting codes (HQECC) have replicated some interesting features of the correspondence. In this work we construct new HQECCs built from random stabilizer tensors that describe a duality between models encompassing local Hamiltonians whilst exactly obeying the Ryu-Takayanagi entropy formula for all boundary regions. We also obtain complementary recovery of local bulk operators for any boundary bipartition. Existing HQECCs have been shown to exhibit these properties individually, whereas our mathematically rigorous toy models capture these features of AdS/CFT simultaneously, advancing further towards a complete construction of holographic duality.