Mean-field entanglement transitions in random tree tensor networks

Javier Lopez-Piqueres; Brayden Ware; Romain Vasseur

doi:10.1103/physrevb.102.064202

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arXiv · 2003.01138

Mean-field entanglement transitions in random tree tensor networks

Javier Lopez-Piqueres·Brayden Ware·Romain Vasseur

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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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cond-mat.stat-mech cond-mat.dis-nn cond-mat.str-el quant-ph

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BibTeX RIS

Javier Lopez-Piqueres, Brayden Ware, Romain Vasseur. 2020-03-02. Mean-field entanglement transitions in random tree tensor networks. https://doi.org/10.1103/physrevb.102.064202

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