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Continuous measurement makes local particle-number fluctuations nonuniform on a Fibonacci free-fermion chain, with a crossover from quasiperiodic long-range order to local bond environments as measurement strength grows.

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2026-07-11 23:52 UTC pith:XAOW6TYW

load-bearing objection Clean numerical demonstration that continuous measurement makes local density fluctuations nonuniform and quasiperiodic-specific, with a clear long-range-to-local crossover.

arxiv 2607.03799 v1 pith:XAOW6TYW submitted 2026-07-04 cond-mat.stat-mech cond-mat.dis-nncond-mat.quant-gasquant-ph

Measurement-induced spatially nonuniform fluctuations of the local particle number and their crossover in a quasiperiodic free-fermion chain

Toranosuke Matsubara , Kazuki Yamamoto This is my paper
classification cond-mat.stat-mech cond-mat.dis-nncond-mat.quant-gasquant-ph
keywords continuous measurementFibonacci chainquasiperiodic free fermionslocal particle-number fluctuationsmeasurement-induced crossoverperpendicular-space analysisconnected correlation functionsquantum trajectories
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies free fermions hopping on a Fibonacci (quasiperiodic) chain while the local particle number at every site is continuously monitored. In the unitary limit those fluctuations are spatially uniform; once measurement is turned on they become nonuniform. For weak measurement the spatial pattern of the fluctuations tracks the long-range aperiodic order of the lattice; for strong measurement the same fluctuations collapse onto values fixed only by the two neighboring bond lengths around each site. The same crossover appears in connected density–density correlation functions. The authors argue that this measurement-induced change of spatial structure is a genuine quasiperiodic phenomenon, absent in both periodic chains and periodic approximants, and that it can be read out with cold-atom quantum-gas microscopes.

Core claim

Under continuous monitoring the steady-state fluctuations of the local particle number on a Fibonacci free-fermion chain develop a spatially nonuniform pattern that is absent in the unitary limit. Weak measurement produces a continuous modulation that reflects the quasiperiodic long-range order; stronger measurement drives a crossover in which the fluctuations become piecewise constant, determined solely by the local environment of each site (ℓℓ versus ℓs bonds). The identical crossover is visible in connected correlation functions when they are examined in perpendicular space.

What carries the argument

Perpendicular-space analysis of the Fibonacci chain: each physical site is mapped to a coordinate inside a strip whose sub-regions label identical local bond environments. Plotting fluctuations (or correlations) against this coordinate makes the measurement-driven crossover—from continuous quasiperiodic modulation to discrete local-environment clusters—visible by eye.

Load-bearing premise

That the nonuniform patterns and the weak-to-strong crossover seen at system sizes up to L=120 survive in the thermodynamic limit and are not finite-size or sampling artifacts.

What would settle it

Compute the same local-number fluctuations for a sequence of larger Fibonacci chains (or higher-order approximants) at fixed weak and strong measurement strengths; if the continuous modulation at weak γ collapses into a few discrete values already at moderate L, or if the strong-γ clusters fail to remain constant inside each local-environment region, the claimed crossover is an artifact.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 4 minor

Summary. The paper studies free fermions on a Fibonacci chain under continuous local-number monitoring via the stochastic Schrödinger equation. In the unitary limit the local particle-number fluctuations Fi are spatially uniform (Fi = 0.25). Under continuous measurement they become nonuniform: for weak γ the spatial profile of Fi (and of connected correlators Cavg) tracks the quasiperiodic long-range order, while for strong γ it collapses to discrete values fixed by the two adjacent bond types (ℓℓ versus ℓs). The crossover is demonstrated by physical-space profiles, by perpendicular-space clustering into regions VRn defined solely by the lattice geometry, and by comparison with a periodic chain and a 2/1 approximant (Appendix A). The same measurement-induced crossover appears in connected correlation functions at several distances.

Significance. The work isolates a measurement-induced phenomenon that is intrinsic to quasiperiodicity rather than to disorder or homogeneity. The perpendicular-space analysis cleanly separates long-range-order signatures from local-environment effects, and the control calculations (periodic chain + approximant) make the claim falsifiable. The observables (Fi and Cavg) are experimentally accessible with quantum-gas microscopes and continuous monitoring, so the results supply a concrete, testable prediction for ultracold-atom quasicrystal platforms. The Gaussian-state numerics are standard and correctly implemented; the data are openly available.

minor comments (4)
  1. Error bars or trajectory-to-trajectory variance are never shown on Fi or Cavg (Figs. 4–9). Even a brief statement of the typical statistical uncertainty for the L = 120, 1000-trajectory data would strengthen the claim that the cluster structure is resolved.
  2. Sec. III B asserts that the crossover trend is robust under system-size increase “(not shown)”. A short supplementary panel or a sentence quantifying the residual finite-size drift of the cluster widths would remove any residual doubt.
  3. Fig. 5 caption and surrounding text note residual left–right asymmetry attributed to finite size; a single sentence confirming that the thermodynamic-limit symmetry is recovered for the largest L would be helpful.
  4. Typographical: “contiuous” in Appendix A; “physicaland” missing hyphen in the abstract; occasional inconsistent spacing around γ/Js.

Circularity Check

0 steps flagged

No circularity: central claims are direct numerical outputs of the stochastic Schrödinger equation on the Fibonacci chain, with lattice geometry fixed independently of the measured Fi and Cavg.

full rationale

The paper defines the Fibonacci lattice via the cut-and-project method (Sec. II A, Eqs. 1–4 and Fig. 1), the free-fermion Hamiltonian (Eq. 5), and continuous monitoring via the stochastic Schrödinger equation (Eq. 6). Local fluctuations Fi (Eq. 7) and connected correlators Ci,j / Cavg (Eqs. 13–14) are then computed as ensemble averages over quantum trajectories of Gaussian states, starting from the half-filled Néel state. Spatial nonuniformity, the weak-to-strong measurement crossover, and the corresponding patterns in perpendicular space (regions VR_n defined solely by local bond sequences Φ(i−R,i+R), Eqs. 8–12, 15–31) are read off the resulting numerical profiles (Figs. 2–9). No parameters are fitted to data and then re-used as predictions; the perpendicular-space partition is geometry-only and independent of the values of Fi or Cavg; control calculations on the periodic chain and the 2/1 approximant (Appendix A) are likewise direct simulations. Self-citations (e.g., prior work on entanglement in the same setting) supply context but are not load-bearing for the fluctuation/crossover claims. The derivation chain is therefore self-contained numerical observation, not circular.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The work rests on standard free-fermion and quantum-trajectory machinery plus the geometric definition of the Fibonacci chain. No new dynamical equations or free parameters are fitted to produce the central claim; the only free choices are conventional numerical parameters (hopping ratio, measurement strengths, system sizes).

free parameters (3)
  • Jℓ/Js = 0.4
    Fixed by hand to 0.4 to realize a clear quasiperiodic modulation; the qualitative claims are stated to hold for other ratios as well.
  • measurement strengths γ/Js = 0.03–5
    Discrete set of values (0.03–5) chosen to illustrate weak-to-strong crossover; not fitted to data.
  • system sizes L and trajectory counts = L≤120, Ntraj≤1000
    L up to 120, 500–1000 trajectories; conventional numerical cut-offs.
axioms (4)
  • domain assumption Time evolution under continuous local-number monitoring is given by the stochastic Schrödinger equation (6) with Poissonian jumps ξj,t.
    Standard quantum-trajectory unraveling of continuous measurement (Daley 2014 and references therein); invoked throughout Sec. II B.
  • domain assumption Free-fermion Gaussian states remain closed under the monitored dynamics, permitting efficient simulation.
    Standard for non-interacting fermions; used to justify the numerical method (Sec. II B).
  • standard math The Fibonacci chain is generated by the cut-and-project method with irrational slope arctan(1/τ).
    Geometric definition of the quasiperiodic lattice (Sec. II A).
  • domain assumption In the steady state a sufficient number of trajectories yields ⟨ni⟩≃0.5, so Fi≃0.5−⟨ni⟩2.
    Used to interpret fluctuations (Sec. III A); verified numerically in Fig. 3.

pith-pipeline@v1.1.0-grok45 · 23918 in / 2493 out tokens · 24046 ms · 2026-07-11T23:52:15.294358+00:00 · methodology

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read the original abstract

We study continuously monitored dynamics of a quasiperiodic free-fermion chain defined on a Fibonacci lattice. We focus on fluctuations of the local particle number, which exhibit a spatially uniform distribution in the unitary limit. Remarkably, we demonstrate that they exhibit a nonuniform spatial pattern originating from the quasiperiodic long-range order under continuous measurement. Furthermore, employing both physicaland perpendicular-space analyses, we elucidate that measurement-induced crossover emerges in fluctuations due to the interplay between the incommensurate modulation and the continuous measurement. While weak measurement yields a distribution reflecting the long-range spatial structure of the quasiperiodic system, an increase in measurement strength alters the distribution into one dominated by the local environment of each site. We also elucidate that the measurement-induced crossover emerges in other physical quantities such as connected correlation functions. These findings offer insights into nonequilibrium quasiperiodic phenomena emerging in continuously monitored dynamics.

Figures

Figures reproduced from arXiv: 2607.03799 by Kazuki Yamamoto, Toranosuke Matsubara.

Figure 1
Figure 1. Figure 1: FIG. 1. The Fibonacci chain obtained by cutting and projecting a [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Spatial distribution of the local particle number with respect [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Numerical results for the dynamics of fluctuations of the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Spatial distribution of fluctuations of the local particle num [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Spatial average of fluctuations of the local particle number [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Spatial distribution of fluctuations of the local particle num [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: shows C avg L/2,r as a function of distance |x(L/2)+r − x(L/2)−r |/2. While the periodic system exhibits a monotonic decay of the correlation function irrespective of the measure￾ment strength [see [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Distribution of correlation functions in the quasiperiodic chain with respect to [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Distribution of the correlation function [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Schematic illustration of the 2 [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Spatial profile of fluctuations of the local particle number on [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗

discussion (0)

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