Measurement-induced phase transition in the dynamics of entanglement

We study the dynamics of quantum entanglement in a many-body system that undergoes unitary evolution punctuated by projective measurements. We show that when these measurements occur randomly with a finite rate per degree of freedom, there is a critical measurement rate that separates "entangling" and "disentangling" phases. The entangling phase is characterized by a linear growth of the entanglement entropy with time that leads to volume-law entanglement, while in the disentangling phase the entanglement entropy takes a constant, area-law value. We demonstrate this dynamical transition using numerics and a mapping to classical percolation that becomes exact in certain limits.