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Tensor networks provide a natural framework for studying bulk-to-boundary or holographic correspondences. In this talk, we will explore the holographic properties of random tensor networks with large bond dimensions. We find that they realize many of the interesting structural features of the AdS/CFT correspondence in quantum gravity: Entanglement entropies of boundary subsystem correspond to minimal domain walls in the bulk, and the physics in the domain is encoded faithfully in the boundary subsystem. Increasing the entanglement in the bulk ultimately creates the analog of a black hole, with an associated Hawking-Page phase transition. All this can be understood by mapping the statistical properties of random tensors to the partition function of classical ferromagnetic Ising models. From the perspective of quantum information theory, random tensor networks implement quantum error-correcting codes with interesting locality properties, and their emergence can be understood as an assisted form of entanglement distillation.

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Michael Walter, Stanford University
Seminar room 0.03, ETP
Contact: not specified