Purification Timescales in Monitored Fermions

• URL: http://arxiv.org/abs/2303.12216v1
• Date: Tue, 21 Mar 2023 22:29:31 GMT
• Title: Purification Timescales in Monitored Fermions
• Authors: Hugo L\'oio, Andrea De Luca, Jacopo De Nardis, Xhek Turkeshi
• Abstract summary: We study Majorana and Dirac circuits with $mathbbZ$ and U(1) symmetries. We find the mixed phase is characterized by $tau_Psim Lalpha(p)$, with a continuously varying exponent $alpha(p)1$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\alpha(p)<1$.

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