Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions

Abstract

Continuous monitoring of one-dimensional free fermionic systems can generate phenomena reminiscent of quantum criticality, such as logarithmic entanglement growth, algebraic correlations, and emergent conformal invariance, but in a nonequilibrium setting. However, whether these signatures reflect a genuine phase of nonequilibrium quantum matter or persist only over finite length scales is an active area of research. We address this question in a free fermionic chain subject to continuous monitoring of lattice-site occupations. An unraveling phase $\ddot{I}†$ interpolates between measurement schemes, corresponding to different stochastic unravelings of the same Lindblad master equation: For $\ddot{I}†=0$, measurements disentangle lattice sites, while for $\ddot{I}†=\ddot{I}€/2$ they act as unitary random noise, yielding volume-law steady-state entanglement. Using replica Keldysh field theory, we obtain a nonlinear sigma model describing the long-wavelength physics. This analysis shows that for $0\le \ddot{I}†<\ddot{I}€/2$, entanglement ultimately obeys an area law, but only beyond the exponentially large scale $\ln (l_{\ddot{I}†,\ast })\sim J/[{\hat{I}}^3\cos (\ddot{I}†)]$, where $J$ is the hopping amplitude and ${\hat{I}}^3$ the measurement rate. Resolving $l_{\ddot{I}†,\ast }$ in numerical simulations is difficult for ${\hat{I}}^3/J\to 0$ or $\ddot{I}†\to \ddot{I}€/2$. However, the theory also predicts that critical-like behavior appears below a crossover scale that grows only algebraically in $J/{\hat{I}}^3$, making it numerically accessible. Our simulations confirm these predictions, establishing the absence of measurement- or unraveling-induced entanglement transitions in this model.

24 pages, 5 figures

References in corpus (3)

• Universality in driven open quantum matter
• Entanglement dynamics of monitored noninteracting fermions on graphics processing units
• Entanglement phases and phase transitions in monitored free fermion system due to localizations

Cited by in corpus (1)

• Replica Keldysh field theory of quantum-jump processes: General formalism and application to imbalanced and inefficient fermion counting