Purification Dynamics in a Continuous-time Hybrid Quantum Circuit Model

We introduce a continuous time model of many-body quantum dynamics based on infinitesimal random unitary operations, combined with projective measurements. We consider purification dynamics in this model, where the system is initialized in a mixed state, which then purifies over time as a result of the measurements. By mapping our model to a family of effective 1D quantum Hamiltonians, we are able to derive analytic expressions that capture how the entropy of the system decays in time. Our results confirm the existence of two distinct dynamical phases, where purification occurs over a timescale that is exponential vs. constant in system size. We compare our analytic expressions for this microscopic model to results derived from field theories that are expected to capture such measurement-induced phase transitions, and find quantitative agreement between the two.