Mathematical analysis

Physics

Renormalization

Holography

Computer science

Theoretical physics

Quantum mechanics

Quantum entanglement

Pure mathematics

Mathematics

Mathematical physics

Tensor (intrinsic definition)

Boundary (topology)

Ansatz

Class (philosophy)

Artificial intelligence

Quantum

Physical Review Letters

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 multiscale entanglement renormalization ansatz (MERA), in that they describe quantum states with algebraic correlation functions, have free variational parameters, and are efficiently contractible. Yet, unlike the 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.

Hyperinvariant Tensor Networks and Holography