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arxiv: 2605.10758 · v2 · pith:WN3F4J25new · submitted 2026-05-11 · 🪐 quant-ph · cond-mat.dis-nn

No measurement induced phase transition in the entanglement dynamics of monitored non-interacting one-dimensional fermions in a disordered or quasiperiodic potential

Can Yin , Fan Bo , Antonio M. Garc\'ia-Garc\'ia This is my paper

Pith reviewed 2026-05-20 22:29 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.dis-nn
keywords measurement induced phase transitionentanglement entropynon-interacting fermionsdisordered potentialquasiperiodic potentialarea lawnonlinear sigma model
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The pith

Monitored non-interacting one-dimensional fermions in disordered or quasiperiodic potentials remain in an area-law entanglement phase for any monitoring strength.

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

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.

Core claim

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.

What carries the argument

Mapping onto a nonlinear sigma model that encodes the symmetry change from BDI to AIII and yields the correlation length for the disordered case.

If this is right

  • 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.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • 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.

Load-bearing premise

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.

What would settle it

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.

Figures

Figures reproduced from arXiv: 2605.10758 by Antonio M. Garc\'ia-Garc\'ia, Can Yin, Fan Bo.

Figure 1
Figure 1. Figure 1: Correlation length lcor as a function of the disorder strength W ∈ [0.01, 0.225] at a monitoring strength γ = 0.6 for the QSD protocol. We average over both disorder (at least 3 ensembles) and quantum trajectories (at least 10 trajectories for a fixed disorder). As is observed, the correlation length lcor shows a logarithmic growth with the disorder strength W, indicating that larger system sizes are neces… view at source ↗
Figure 2
Figure 2. Figure 2: Correlation length lcor as a function of the measure￾ment strength γ for the disordered system under the QSD proto￾col. For most data points, we use the system size L = 8192, while larger system sizes are employed when the correlation length approaches the system size, i.e. L = 10000: (W = 0.25, γ = 0.55), (W = 0.5, γ = 0.575), (W = 0.75, γ = 0.55); L = 14000: (W = 0.5, γ = 0.55); L = 18000: (W = 0.25, γ =… view at source ↗
Figure 3
Figure 3. Figure 3: Correlation length lcor as a function of the mea￾surement strength γ for the quasiperiodic system (V = 0.5) under the PM protocol. The solid lines correspond to the ana￾lytical predictions Eqs. (5), (6). For the quasiperiodic system, the numerical results are consistent with the AIII scaling Eq. (6). For comparison, data for the clean limit (V = 0), class BDI, are extracted from Fig.1(b) of Ref. [53], yiel… view at source ↗
read the original abstract

We show that the entanglement entropy (EE) of one-dimensional (1d) non-interacting fermions with $U(1)$ symmetry in the presence of a disordered or quasi-periodic potential in which the occupation number is being monitored by homodyne or projective protocols is always in an area-law phase so no measurement induced phase transition (MIPT) occurs. The reason for the previously claimed MIPT in these systems was a finite size effect related to the fact that the maximum lattice size $L \sim 500$ was of the order of the correlation length. By increasing the system size up to $L \leq 18000$, employing Graphics Processing Unit (GPU), and performing a careful finite size scaling analysis, we find that the critical monitoring strength is consistent with zero so no MIPT occurs. For the disordered case, these numerical results are fully supported by an analytical calculation based on mapping the problem onto a nonlinear sigma model (NLSM) that confirms the absence of the MIPT for any monitoring or disorder strength. The effect of disorder is captured by a change of symmetry, from BDI to AIII, which results in an enhanced correlation length in the weak disorder limit and, by an effective monitoring strength that increase linearly with disorder.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

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.

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 (2)
  1. [Numerical results and finite-size scaling] 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.
  2. [Analytical NLSM calculation] 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.
minor comments (2)
  1. [Methods] 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.
  2. [Figures] 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.

Simulated Author's Rebuttal

2 responses · 0 unresolved

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.

read point-by-point responses

  1. Referee: 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.

    Authors: 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: partial

  2. Referee: 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.

    Authors: 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: yes

Circularity Check

0 steps flagged

No significant circularity: numerics and NLSM mapping are independent of the target claim

full rationale

The paper derives the absence of MIPT from two independent lines: (1) direct computation of entanglement entropy on systems up to L=18000 followed by standard finite-size scaling to extrapolate the apparent critical monitoring rate to zero, and (2) an analytical mapping of the disordered case onto a nonlinear sigma model that changes the symmetry class (BDI to AIII) and produces an effective monitoring strength linear in disorder strength. Neither line reduces by construction to its own inputs; the scaling ansatz is applied to externally computed data rather than defining the critical point tautologically, and the NLSM is presented as a first-principles symmetry analysis rather than a self-citation or ansatz smuggled from prior work by the same authors. The central claim therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the NLSM mapping for the disordered case and on the assumption that finite-size effects fully explain prior apparent transitions. No free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Mapping the monitored fermion problem onto a nonlinear sigma model with symmetry class changed from BDI to AIII
    Invoked to analytically confirm absence of MIPT for any monitoring or disorder strength in the disordered case.

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    Then we try to integrate out the fastΦ f field, we first perform the expansion of Wµ ≡ −iU † f(∂µUf): Wµ =∂ µΦf − i 2 [Φf , ∂µΦf]− 1 6 [Φf ,[Φ f , ∂µΦf]] +O(Φ 4 f)

    =−(∂ µU0)U † 0 ,(∂ µU † f)Uf =−U † f(∂µUf), the last two fast-slow correlated term merge into 2DP µ Tr h (∂µU0)U † 0 U † f(∂µUf) i . Then we try to integrate out the fastΦ f field, we first perform the expansion of Wµ ≡ −iU † f(∂µUf): Wµ =∂ µΦf − i 2 [Φf , ∂µΦf]− 1 6 [Φf ,[Φ f , ∂µΦf]] +O(Φ 4 f). and we expand the non-zero interaction vertex inS 0 of thre...

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