Purification Timescales in Monitored Fermions

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 ${\tau }_P\sim L\ln L$. At $1\ll t\ll {\tau }_P$ 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 ${\tau }_P\sim L^{\alpha (p)}$, with a continuously varying exponent $\alpha (p)<1$.

7 pgase, 3 figures, 3 pages of supplementary material