Purification timescales in monitored fermions
Hugo Lóio, A. De Luca, Jacopo De Nardis, Xhek Turkeshi
Abstract
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 ${\mathbb{Z}}_{2}$ and U(1) symmetries, respectively. In the first case, we demonstrate the mixed phase of $L$ sites has a purification timescale that scales as ${\ensuremath{\tau}}_{P}\ensuremath{\sim}LlnL$. At $1\ensuremath{\ll}t\ensuremath{\ll}{\ensuremath{\tau}}_{P}$ 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 ${\ensuremath{\tau}}_{P}\ensuremath{\sim}{L}^{\ensuremath{\alpha}(p)}$, with a continuously varying exponent $\ensuremath{\alpha}(p)<1$.