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

• URL: http://arxiv.org/abs/2510.19459v1
• Date: Wed, 22 Oct 2025 10:46:07 GMT
• Title: Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions
• Authors: Clemens Niederegger, Tatiana Vovk, Elias Starchl, Lukas M. Sieberer,
• Abstract summary: An unraveling phase $varphi$ interpolates between measurement schemes, corresponding to different unravelings of the same Lindblad master equation.<n>For $0 leq varphi pi/2$, entanglement ultimately obeys an area law, but only beyond the exponentially large scale.<n>Our analysis shows that for $0 leq varphi pi/2$, entanglement ultimately obeys an area law, but only beyond the exponentially large scale.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\varphi$ interpolates between measurement schemes, corresponding to different stochastic unravelings of the same Lindblad master equation: For $\varphi = 0$, measurements disentangle lattice sites, while for $\varphi = \pi/2$ 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 $0 \leq \varphi < \pi/2$, entanglement ultimately obeys an area law, but only beyond the exponentially large scale $\ln(l_{\varphi,*}) \sim J/[\gamma \cos(\varphi)]$, where $J$ is the hopping amplitude and $\gamma$ the measurement rate. Resolving $l_{\varphi, *}$ in numerical simulations is difficult for $\gamma/J \to 0$ or $\varphi \to \pi/2$. However, the theory also predicts that critical-like behavior appears below a crossover scale that grows only algebraically in $J/\gamma$, making it numerically accessible. Our simulations confirm these predictions, establishing the absence of measurement- or unraveling-induced entanglement transitions in this model.

Related papers

• Theta-term in Russian Doll Model: phase structure, quantum metric and BPS multifractality [45.88028371034407]
  We investigate the phase structure of the deterministic and disordered versions of the Russian Doll Model (RDM)<n>We find the pattern of phase transitions in the global charge $Q(theta,gamma)$, which arises from the BA equation.<n>We conjecture that the Hamiltonian of the RDM model describes the mixing in particular 2d-4d BPS sector of the Hilbert space.
  arXiv  Detail & Related papers  (2025-10-23T17:25:01Z)
• Mesoscopic Fluctuations and Multifractality at and across Measurement-Induced Phase Transition [46.176861415532095]
  We explore statistical fluctuations over the ensemble of quantum trajectories in a model of two-dimensional free fermions.<n>Our results exhibit a remarkable analogy to Anderson localization, with $G_AB$ corresponding to two-terminal conductance.<n>Our findings lay the groundwork for mesoscopic theory of monitored systems, paving the way for various extensions.
  arXiv  Detail & Related papers  (2025-07-15T13:44:14Z)
• Monitored fermions with conserved $\mathrm{U}(1)$ charge [0.0]
  We study measurement-induced phases of free fermion systems with U(1) symmetry.<n>We derive a field theory description for the purity and bipartite entanglement at large space and time scales.
  arXiv  Detail & Related papers  (2024-07-10T20:53:47Z)
• Diffusive entanglement growth in a monitored harmonic chain [0.0]
  We find that entanglement grows diffusively ($S sim t1/2$) for a large class of initial Gaussian states. We propose a modified quasi-particle picture which accounts for all of these main features and agrees quantitatively well with our essentially exact numerical results.
  arXiv  Detail & Related papers  (2024-03-06T20:07:25Z)
• Ancilla quantum measurements on interacting chains: Sensitivity of entanglement dynamics to the type and concentration of detectors [46.76612530830571]
  We consider a quantum many-body lattice system that is coupled to ancillary degrees of freedom (detectors'') We explore the dynamics of density and of entanglement entropy in the chain, for various values of $rho_a$ and $M$.
  arXiv  Detail & Related papers  (2023-11-21T21:41:11Z)
• Measurement-induced phase transition for free fermions above one dimension [46.176861415532095]
  Theory of the measurement-induced entanglement phase transition for free-fermion models in $d>1$ dimensions is developed. Critical point separates a gapless phase with $elld-1 ln ell$ scaling of the second cumulant of the particle number and of the entanglement entropy.
  arXiv  Detail & Related papers  (2023-09-21T18:11:04Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• Nonlinear sigma models for monitored dynamics of free fermions [0.0]
  We derive descriptions for measurement-induced phase transitions in free fermion systems. We use the replica trick to map the dynamics to the imaginary time evolution of an effective spin chain. This is a nonlinear sigma model for an $Ntimes N$ matrix, in the replica limit $Nto 1$.
  arXiv  Detail & Related papers  (2023-02-24T18:56:37Z)
• Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models [77.34726150561087]
  We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model.
  arXiv  Detail & Related papers  (2021-02-02T13:56:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.