Entanglement Phase Transitions in Measurement-Only Dynamics

Abstract

Unitary circuits subject to repeated projective measurements can undergo an entanglement transition as a function of the measurement rate. This transition is generally understood in terms of a competition between the scrambling effects of unitary dynamics and the disentangling effects of measurements. We find that, surprisingly, entanglement transitions are possible even in the absence of scrambling unitary dynamics. We illustrate this phenomenon in models where the unitary dynamics is non-scrambling, as well as models where the dynamics is entirely due to local few-site measurements. This opens the door to a vast landscape of measurement-only models, in which the ``scrambling'' and ``un-scrambling'' effects that drive the entanglement transition are not separable into distinct physical processes. We show numerical results on the entanglement phase diagrams, critical points, locality, and quantum code properties of some of these measurement-only models. We find that an entangling (volume-law) phase is the default outcome, while disentangling (area-law) phases are possible in the presence of special restrictions on the size or commutativity of the measurements. We propose `frustration' of the measurement ensemble as the principle driving the entanglement transition in this class of dynamics.