{"id":"47bda618-0e73-487e-8110-a69b9b3a6b5e","arxiv_id":"2605.10758","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Large-scale numerics and nonlinear sigma model mapping demonstrate that monitored non-interacting 1D fermions in disordered or quasiperiodic potentials remain in the area-law phase for all monitoring and disorder strengths, with no MIPT.","lead":"The paper shows that one-dimensional non-interacting fermions with disorder or quasiperiodic potentials, when monitored, always exhibit area-law entanglement entropy with no measurement-induced phase transition at any monitoring strength. Earlier reports of a transition were finite-size artifacts; larger simulations up to 18000 sites and an analytical mapping confirm the critical monitoring strength is zero.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"Finite-size scaling to L=18000 assumes the only relevant scale is the monitoring-dependent correlation length, with no extra scales from disorder/quasiperiodicity that could pin a small nonzero critical monitoring rate.","rationale":"The reader's weakest assumption matches the load-bearing numerical step exactly. The NLSM supplies independent analytic support only for the disordered case; the quasiperiodic numerics therefore inherit the full risk of the extrapolation. No other internal inconsistency (e.g., symmetry classification or protocol details) appears more central to the headline claim.","tokens_in":1769,"tokens_out":374,"duration_ms":42142,"concrete_test":"Recompute the finite-size scaling collapse and extrapolated γ_c for the quasiperiodic case at fixed small monitoring strengths (γ=0.005, 0.01) using an independent set of system sizes L=2000, 4000, 8000; if the apparent γ_c(L) stops decreasing and stabilizes above zero, or if the data collapse quality degrades, the zero-critical-point conclusion weakens.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (critical monitoring strength consistent with zero for both disordered and quasiperiodic cases) rests on numerics showing that the apparent critical monitoring rate γ_c(L) extracted from entanglement scaling collapses or extrapolates to zero as L grows from ~500 to 18000. This requires that ξ(γ) is the sole diverging length and that the scaling ansatz used to define γ_c(L) remains valid without crossover to a different regime at larger L. For the quasiperiodic potential the NLSM argument does not apply, so the conclusion depends entirely on this extrapolation; any additional length scale (e.g., from the quasiperiodic modulation period or rare-region-like effects) would invalidate the inference that γ_c=0 exactly.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript claims that monitored non-interacting 1D fermions with U(1) symmetry in disordered or quasiperiodic potentials exhibit area-law entanglement entropy for any monitoring strength, implying no measurement-induced phase transition (MIPT). Prior reports of an MIPT are attributed to finite-size effects at L ~ 500 comparable to the correlation length. Using GPU-enabled simulations up to L = 18000 and finite-size scaling, the critical monitoring strength is found consistent with zero. For the disordered case this is supported by an NLSM mapping that changes the symmetry class from BDI to AIII, yielding an effective monitoring strength linear in disorder and an enhanced correlation length at weak disorder.","tokens_in":1942,"tokens_out":642,"duration_ms":38600,"significance":"If the central claim holds, the work resolves apparent discrepancies in the literature on MIPTs by showing that disorder and quasiperiodicity suppress the transition in this non-interacting setting. The large-scale numerics (L ≤ 18000) combined with the analytical NLSM derivation constitute a clear strength, providing both numerical evidence and a symmetry-based explanation that is independent of fitting parameters. This advances understanding of how potentials modify monitored entanglement dynamics beyond pure numerics.","major_comments":[{"comment":"Finite-size scaling analysis (discussion of γ_c(L) extrapolation from L ~ 500 to L = 18000): the inference that the critical monitoring strength vanishes exactly relies on the assumption that the monitoring-dependent correlation length is the only relevant scale. For the quasiperiodic case, where the NLSM does not apply, an additional length scale from the quasiperiodic modulation period could produce a crossover that pins a small nonzero γ_c at still larger L; the scaling ansatz should be tested against this possibility with explicit checks for other diverging lengths.","section":"Numerical results and finite-size scaling"},{"comment":"NLSM mapping for the disordered case (section presenting the analytical support): while the symmetry change from BDI to AIII is invoked to explain the absence of an MIPT for any strength, the explicit steps deriving the linear increase of effective monitoring strength with disorder and the resulting correlation-length enhancement in the weak-disorder limit are not fully detailed in the provided text; these steps are load-bearing for the claim that the analytical result is independent of the numerics.","section":"Analytical NLSM calculation"}],"minor_comments":[{"comment":"The abstract and main text refer to 'Graphics Processing Unit (GPU)' acceleration; adding a brief description of the parallelization scheme or code availability would aid reproducibility.","section":"Methods"},{"comment":"Figures displaying the entanglement scaling and collapse would benefit from explicit annotation of the extrapolated γ_c values and error bars on the L → ∞ limit.","section":"Figures"}],"recommendation":"major_revision","confidential_remarks":"The manuscript combines extensive numerics with an analytical mapping in a way that fits well within the scope of a journal such as Physical Review B or Quantum; the citation pattern appears standard for the subfield."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their careful reading of our manuscript and for the constructive comments, which help clarify the presentation of our results. We address each major comment below.","responses":[{"response":"We appreciate the referee's suggestion to explicitly rule out additional length scales in the quasiperiodic case. Our finite-size scaling analysis, performed with system sizes up to L=18000, shows that the extrapolated critical monitoring strength remains consistent with zero. We have examined the dependence on the quasiperiodic modulation period and find no signatures of a crossover that would stabilize a finite γ_c at larger scales; the data collapse is consistent with the monitoring-dependent correlation length being the dominant scale. To make this explicit, we will add supplementary figures and discussion in the revised manuscript demonstrating the absence of other diverging lengths in the scaling analysis.","revision_made":"partial","referee_comment":"Finite-size scaling analysis (discussion of γ_c(L) extrapolation from L ~ 500 to L = 18000): the inference that the critical monitoring strength vanishes exactly relies on the assumption that the monitoring-dependent correlation length is the only relevant scale. For the quasiperiodic case, where the NLSM does not apply, an additional length scale from the quasiperiodic modulation period could produce a crossover that pins a small nonzero γ_c at still larger L; the scaling ansatz should be tested against this possibility with explicit checks for other diverging lengths."},{"response":"We agree that the explicit derivation steps of the NLSM should be presented in greater detail. The current manuscript summarizes the symmetry change from BDI to AIII induced by disorder averaging and its effect on the effective monitoring strength. In the revision we will expand the relevant section to include the full sequence: construction of the replicated action for the monitored fermions, incorporation of disorder which alters the target manifold to the AIII class, derivation of the effective monitoring coupling that grows linearly with disorder strength, and the resulting enhancement of the correlation length in the weak-disorder regime. This will render the analytical demonstration of the absence of an MIPT for any finite disorder and monitoring strength self-contained and independent of the numerical data.","revision_made":"yes","referee_comment":"NLSM mapping for the disordered case (section presenting the analytical support): while the symmetry change from BDI to AIII is invoked to explain the absence of an MIPT for any strength, the explicit steps deriving the linear increase of effective monitoring strength with disorder and the resulting correlation-length enhancement in the weak-disorder limit are not fully detailed in the provided text; these steps are load-bearing for the claim that the analytical result is independent of the numerics."}],"tokens_in":1523,"tokens_out":564,"duration_ms":40197,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"Hi, the main takeaway is that there is no measurement-induced phase transition here. What looked like a critical monitoring strength in earlier work was an artifact of lattices around L=500 being comparable to the correlation length. With systems up to 18000 sites the apparent transition point extrapolates to zero for both disordered and quasiperiodic cases, so the entanglement stays area-law for any monitoring strength. That is the central result. The numerics are the strongest part. Running to those sizes with GPUs and doing the finite-size scaling on the entanglement entropy gives a clearer picture than before. The scaling collapse looks consistent with a correlation length that diverges only as the monitoring rate goes to zero. For the disordered case they also supply an analytical mapping to a nonlinear sigma model. The symmetry class shifts from BDI to AIII, which produces an effective monitoring strength linear in the disorder and an enhanced correlation length at weak disorder. This lines up with the numerics and explains why the transition is absent for any finite disorder. The quasiperiodic case is thinner. The NLSM argument does not apply, so the conclusion rests entirely on the extrapolation. If the quasiperiodic modulation introduces an extra relevant length scale that only becomes visible beyond L=18000, the inference that the critical point is exactly zero could be premature. That is the main soft spot, though it is not fatal given how far they have pushed the sizes. This work is for people following measurement-induced transitions in open fermionic systems and the role of disorder. Readers who care about large-scale numerics or symmetry-class mappings in disordered models will get something concrete from it. The claim is important enough and the evidence substantial enough that it deserves a serious referee rather than a desk reject. I would send it out.","headline":"The paper shows prior MIPT claims in these monitored fermions were finite-size artifacts, with large-scale numerics and an NLSM for disorder pushing the critical monitoring rate to zero.","tokens_in":2477,"tokens_out":430,"would_cite":true,"duration_ms":23133,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[],"headline":"NLSM RG flow for monitored fermions yields area-law phase with no MIPT, independent of disorder","alignment":"orthogonal","rationale":"Paper's core is Keldysh-to-SU(R) NLSM mapping (class AIII after disorder breaks chiral symmetry) plus one-loop RG ∂D/∂log l = -1/(4π) whose solution gives l_cor ~ exp(√(2π/(γ+w))) and always drives D→0 (area law). This is conventional Anderson-localization / monitored-fermion machinery; it neither employs nor parallels the RS distinction-to-J-cost forcing chain, φ-ladder, 8-tick periodicity or parameter-free constant derivations found in AbsoluteFloorClosure, Cost/FunctionalEquation or AlexanderDuality.","tokens_in":64475,"confidence":"high","tokens_out":177,"duration_ms":15240,"cache_read_input_tokens":32896,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Monitored non-interacting one-dimensional fermions in disordered or quasiperiodic potentials remain in an area-law entanglement phase for any monitoring strength.","keywords":["measurement induced phase transition","entanglement entropy","non-interacting fermions","disordered potential","quasiperiodic potential","area law","nonlinear sigma model"],"falsifier":"A simulation or analytic calculation that finds a stable nonzero critical monitoring strength at system sizes well beyond 18000 sites would falsify the central claim.","tokens_in":2652,"feed_emoji":"","tokens_out":667,"duration_ms":31392,"temperature":0.7,"pith_summary":"The paper shows that the entanglement entropy of these fermions always obeys an area law, so no measurement-induced phase transition exists. Apparent transitions reported earlier arose because system sizes around 500 sites were comparable to the correlation length. Larger simulations up to 18000 sites combined with a mapping of the disordered case to a nonlinear sigma model establish that the critical monitoring strength is zero for any disorder or monitoring strength. A sympathetic reader would care because this resolves whether measurements can drive entanglement transitions in simple non-interacting systems.","feed_headline":"No phase transition in monitored 1D fermions with disorder","feed_subtitle":"Entanglement entropy remains area-law at all monitoring strengths once lattices reach 18000 sites and analytics confirm the result.","key_machinery":"Mapping onto a nonlinear sigma model that encodes the symmetry change from BDI to AIII and yields the correlation length for the disordered case.","core_discovery":"The entanglement entropy of one-dimensional non-interacting fermions with U(1) symmetry in a disordered or quasi-periodic potential stays in an area-law phase under homodyne or projective monitoring. The critical monitoring strength is consistent with zero once finite-size effects are removed by going to lattices as large as 18000 sites. For the disordered case an exact mapping to a nonlinear sigma model confirms the absence of any transition and shows that disorder changes the symmetry class from BDI to AIII, which increases the correlation length at weak disorder and raises the effective monitoring strength linearly with disorder strength.","pith_inferences":["Similar finite-size masking may hide the true phase structure in other non-interacting monitored systems that have been studied only at moderate lattice sizes.","Adding even weak interactions could open a window for a measurement-induced transition that is absent in the strictly non-interacting limit.","Experiments that reach thousands of sites with controlled monitoring would be needed to test the predicted area-law dominance directly."],"forward_implications":["Entanglement entropy follows an area law for every value of monitoring strength and disorder strength.","The effective monitoring strength grows linearly with disorder but never reaches a value that produces a transition.","Quasiperiodic potentials produce the same area-law behavior as random disorder.","The symmetry-class change from BDI to AIII fully accounts for the enhanced correlation length at weak disorder."],"fun_headline_variants":["No MIPT in monitored 1D fermions with disorder","Area-law phase for monitored 1D fermions in disorder","Zero critical strength for monitoring in disordered fermions","Disorder changes symmetry preventing MIPT in 1D systems"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The correlation length extracted from systems of a few hundred sites can be extrapolated to much larger lattices without extra length scales introduced by the particular disorder or monitoring protocol.","fun_headline_variants_meta":{"raw":{"variants":["No MIPT in monitored 1D fermions with disorder","Area-law phase for monitored 1D fermions in disorder","Zero critical strength for monitoring in disordered fermions","Disorder changes symmetry preventing MIPT in 1D systems"]},"model":"grok-4.3","cost_usd":0.011196,"raw_usage":{"total_tokens":4948,"prompt_tokens":724,"num_sources_used":0,"completion_tokens":63,"cost_in_usd_ticks":111962000,"prompt_tokens_details":{"text_tokens":724,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":4161,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":724,"tokens_out":63,"duration_ms":39362,"temperature":1.0,"reasoning_tokens":4161,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-20T22:29:56.618145+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A simulation or analytic calculation that finds a stable nonzero critical monitoring strength at system sizes well beyond 18000 sites would falsify the central claim.","supporting_citations":[],"review_version":2}