Mean-field theory of entanglement transitions from random tree tensor networks

Javier Lopez-Piqueres, Brayden Ware, Romain Vasseur

Published 2020-03-02Version 1

Entanglement phase transitions in quantum chaotic systems subject to projective measurements or 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 entanglement transition. We verify our predictions numerically by computing directly the entanglement of random tree tensor network states.