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Measurement-Driven Phase Transition within a Volume-Law Entangled Phase · Around

2020

Measurement-Driven Phase Transition within a Volume-Law Entangled Phase

Vijay, Sagar

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We identify a phase transition between two kinds of volume-law entangled phases in non-local but few-body unitary dynamics with local projective measurements.

In one phase, a finite fraction of the system belongs to a fully-entangled state, one for which no subsystem is in a pure state, while in the second phase, the steady-state is a product state over extensively many, finite subsystems.
We study this "separability" transition in a family of solvable models in which we analytically determine the transition point, the evolution of certain entanglement properties of interest, and relate this to a mean-field percolation transition.
Since the entanglement entropy density does not distinguish these phases, we introduce the entangling power - which measures whether local measurements outside of two finite subsystems can boost their mutual information - as an order parameter, after considering its behavior in tensor network states, and numerically studying its behavior in a model of Clifford dynamics with measurements.

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