2025/10/22 by Niederegger, Clemens, Vovk, Tatiana, Starchl, Elias +1 · 2 citations
#FOS: Physical sciences #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2510.19459
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 φ interpolates between measurement schemes, corresponding to different stochastic unravelings of the same Lindblad master equation: For φ= 0, measurements disentangle lattice sites, while for φ= π/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 ≤ φ< π/2, entanglement ultimately obeys an area law, but only beyond the exponentially large scale ln(lφ,*) ∼ J/[γcos(φ)], where J is the hopping amplitude and γ the measurement rate. Resolving lφ, * in numerical simulations is difficult for γ/J → 0 or φ→ π/2. However, the theory also predicts that critical-like behavior appears below a crossover scale that grows only algebraically in J/γ, making it numerically accessible. Our simulations confirm these predictions, establishing the absence of measurement- or unraveling-induced entanglement transitions in this model.