Michael Walter

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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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Stanford University
Seminar room 0.03, ETP
Contact: not specified