Mean-field entanglement transitions in random tree tensor networks

Journal Article · Thu Aug 06 00:00:00 EDT 2020 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.102.064202· OSTI ID:1647652

Lopez-Piqueres, Javier ^[1]; Ware, Brayden ^[2]; Vasseur, Romain ^[2]

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1. Univ. of Massachusetts, Amherst, MA (United States); UMass Amherst
2. Univ. of Massachusetts, Amherst, MA (United States)

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. Furthermore, we verify our predictions numerically by computing directly the entanglement of random tree tensor network states.

• Research Organization: Univ. of Massachusetts, Amherst, MA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: SC0019168
• OSTI ID: 1647652
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 6 Vol. 102; ISSN 2469-9950; ISSN 2469-9969
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Cavity methods
Critical phenomena
Entanglement entropy
Quantum entanglement
Replica methods
Tensor network methods