Anomalous purification dynamics in measurement-only quantum circuits

Symmetries play a central role in quantum dynamics and critical phenomena. In measurement-only circuits, the subtle interplay of symmetry and measurement frustration can give rise to an anomalous dynamical regime in the purification of mixed states. Moreover, the exponent z* found from scaling-collapse in this regime is different from that found in the stationary state and in pure-state dynamics, indicating a transient critical scaling regime. By considering generalized cluster models and random stabilizer circuits in one and two dimensions, we give a systematic analysis of the role of symmetry, measurement-frustration, and geometric frustration in determining the existence of the transient scaling regime and the magnitude of z*. Finally, we explore the relationship between the exponent z* and the spread of correlations in real-space via the propagation of mutual information through the circuit.