Measurement-induced quantum phase transition with classically diffusing measurers

The competition between scrambling and projective measurements can lead to measurement-induced phase transitions (MIPT). In this work, we show that the universality class of the MIPT drastically alters when the system is coupled to a diffusing conserved density. Specifically, we consider a 1+1d random Clifford circuit locally monitored by classically diffusing particles (``measurers''). The resulting diffusive correlations of the measurements are a relevant perturbation to the usual space-time random MIPT critical point. We find that the new critical point appears to have a divergent dynamical exponent $z ightarrowinfty$, in some ways resembling infinite-randomness critical points of systems with time-independent quenched randomness. We find ``Griffiths-like'' effects due to long-lived rare space-time regions where, e.g., the diffusive measurers have a lower/higher density, but these are considerably weaker than the Griffiths effects that occur with quenched randomness that produces rare spatial regions with infinite lifetime.