Measurement-induced phase transitions in systems with diffusive dynamics

The competition between scrambling and projective measurements can lead to measurement-induced entanglement phase transitions (MIPT). In this work, we show that the universality class of the MIPT can be drastically altered when the system has a diffusing conserved density. As a numerical tractable model of this, we study a 1+1d random Clifford circuit locally monitored by classically diffusing particles ("measurers"). The resulting diffusive correlations in the measurement density are a relevant perturbation to the usual space-time random MIPT critical point, producing a new universality class for this phase transition. We find "Griffiths-like"effects due to rare space-time regions where, e.g., the diffusive measurers have a low or high density, but these are considerably weaker than the Griffiths effects that occur with quenched randomness that produce rare spatial regions with infinite lifetime.