Journal
PHYSICAL REVIEW B
Volume 102, Issue 6, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.102.064202
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Funding
- U.S. Department of Energy, Office of Science, Basic Energy Sciences [DE-SC0019168]
- Alfred P. Sloan Foundation
- U.S. Department of Energy (DOE) [DE-SC0019168] Funding Source: U.S. Department of Energy (DOE)
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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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