Mean-field entanglement transitions in random tree tensor networks

• URL: http://arxiv.org/abs/2003.01138v2
• Date: Mon, 10 Aug 2020 18:52:02 GMT
• Title: Mean-field entanglement transitions in random tree tensor networks
• Authors: Javier Lopez-Piqueres, Brayden Ware, Romain Vasseur
• Abstract summary: Entanglement phase transitions in quantum chaotic systems have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks. As a function of bond dimension, we find a phase transition separating area-law from logarithmic scaling of the entanglement entropy. Using a mapping onto a replica statistical mechanics model defined on a Cayley tree and the cavity method, we analyze the scaling properties of such transitions. Our approach provides a tractable, mean-field-like example of an entanglement transition. We verify our predictions numerically by computing directly the entanglement of random tree tensor network states.

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