Random tensor networks and holographic entanglement

Tensor networks provide a natural framework for exploring holographic dualities because their entanglement entropies automatically obey an area law. We study the holographic properties of networks of random tensors. We review several interesting structural features of the AdS/CFT correspondence and derive them in our model.  Entropies of random tensor networks satisfy the Ryu-Takayanagi formula for all boundary regions, including corrections due to bulk entanglement. Our method is to interpret random tensor averages as the partition functions of classical ferromagnetic Ising models, so that the minimal surfaces of the Ryu-Takayanagi formula appear as domain walls. Increasing the entanglement of the bulk ultimately creates the analog of a black hole. The bulk-boundary correspondence defined by a random tensor network satisfies an appropriate quantum error correction property known as entanglement wedge reconstruction.  We further study the multipartite entanglement structure of random stabilizer tensor networks and conclude by some remarks about the properties of entanglement entropy in holographic states.

References: 

1. Holographic Duality From Random Tensor Networks arXiv:1601.01694

2. Multipartite Entanglement in Stabilizer Tensor Networks arXiv:1608.02595