Purification timescales in monitored fermions

We investigate the crucial role played by a global symmetry in the purification timescales and the phase transitions of monitored free fermionic systems separating a mixed and a pure phase. Concretely, we study Majorana and Dirac circuits with Z₂ and U (1) symmetries, respectively. In the first case, we demonstrate the mixed phase of L sites has a purification timescale that scales as ₏. At 1₏ the system attains a finite residual entropy, that we use to unveil the critical properties of the purification transition. In contrast, free fermions with U (1) manifest a sublinear purification timescale at any measurement rate and an apparent Berezinskii-Kosterlitz-Thouless criticality. We find the mixed phase is characterized by ₏L^ (p), with a continuously varying exponent (p) <1.