Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions
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| Format: | Preprint |
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2025
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| _version_ | 1866915999481069568 |
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| author | Niederegger, Clemens Vovk, Tatiana Starchl, Elias Sieberer, Lukas M. |
| author_facet | Niederegger, Clemens Vovk, Tatiana Starchl, Elias Sieberer, Lukas M. |
| contents | 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 $0 \leq φ< π/2$, entanglement ultimately obeys an area law, but only beyond the exponentially large scale $\ln(l_{φ,*}) \sim J/[γ\cos(φ)]$, where $J$ is the hopping amplitude and $γ$ the measurement rate. Resolving $l_{φ, *}$ in numerical simulations is difficult for $γ/J \to 0$ or $φ\to π/2$. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_19459 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions Niederegger, Clemens Vovk, Tatiana Starchl, Elias Sieberer, Lukas M. Quantum Physics Statistical Mechanics 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 $0 \leq φ< π/2$, entanglement ultimately obeys an area law, but only beyond the exponentially large scale $\ln(l_{φ,*}) \sim J/[γ\cos(φ)]$, where $J$ is the hopping amplitude and $γ$ the measurement rate. Resolving $l_{φ, *}$ in numerical simulations is difficult for $γ/J \to 0$ or $φ\to π/2$. 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. |
| title | Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2510.19459 |