Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Measurments-induced quantum phase transitions

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Monitoring a free-fermion chain at any nonzero rate forces the stationary entanglement entropy into an area law, making volume-law entanglement a strictly unmeasured limit.

desk verdict Proceedings summary of the authors' PRB; area-law claim plausible but the scaling story is internally inconsistent, so don't cite this version. read the letter →

arxiv 2412.06440 v1 pith:2IQXP56Y submitted 2024-12-09 cond-mat.stat-mech quant-ph

Dragi Karevski , Michele Coppola , Emanuele Tirrito , Mario Collura This is my paper · ORCID
classification cond-mat.stat-mechquant-ph
keywords entanglemententropyprojectivemeasurementsfreefermionsmeasurement-inducedtransitionarealawGaussianstatesquantumdynamics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper studies a one-dimensional chain of free fermions whose local particle density is randomly measured at rate 1/τ, and asks how the entanglement entropy of intervals behaves. It claims that the volume-law phase is absent for any nonzero measurement rate: although the entropy grows logarithmically during the initial transient, its stationary value obeys an area law once the interval is longer than a correlation length ξ(τ) that grows exponentially with τ. The logarithmic scaling found in finite-size simulations is therefore a finite-size effect, not a distinct phase. The authors support this with a scaling collapse of their numerics and analytic quasi-particle arguments.

What carries the argument

The machinery is the two-point correlation matrix C_ij = tr{c^†_i c_j ρ}, which fully characterizes the Gaussian state; unitary evolution rotates it by the matrix R(s), and projective density measurements update it through the nonlinear rules in Eqs. (5) and (6). The paper's central analytical input is the scaling ansatz S_ℓ/(ℓ ln 2) = f(ℓ/τ), with f(x)→1 for x≪1 and f(x)→1/x for x≫1, which is equivalent to an exponentially growing correlation length ξ(τ) ~ $e^{{ατ}}$. This ansatz carries the paper's conclusion that no finite measurement rate produces a volume-law steady state.

What would settle it

A direct test: simulate the same monitored chain for system sizes well beyond L=400 and fix any finite rate 1/τ; if the stationary entanglement entropy S_ℓ for ℓ much larger than the inferred correlation length continues to grow with ℓ, as log ℓ or as a power ℓ^γ, the area-law-at-any-rate claim is false. Equivalently, find a rate where the data collapse onto f(ℓ/τ) breaks down, meaning S_ℓ/(ℓ ln 2) does not tend to 1/x for large x.

Watch

Extended reading notes

Core claim

The central discovery is that local projective measurements of density on a Gaussian fermionic chain do not produce a measurement-induced phase transition between volume-law and area-law entanglement at a nonzero rate. Instead, monitoring at any finite rate 1/τ < ∞ drives the stationary entanglement entropy to an area law ∝ ln ξ(τ) in the thermodynamic limit, with ξ(τ) ~ $e^{{ατ}}$. The paper argues that the volume-law phase survives only at τ = ∞, i.e., with no measurements at all, and that the intermediate logarithmic behavior seen in finite-size data is a crossover controlled by the exponentially large correlation length rather than a genuine phase.

Load-bearing premise

The whole conclusion rests on the assumption that the system has a finite correlation length that grows exponentially with the time between measurements, so that measuring at any nonzero rate eventually puts any large subsystem into an area law; if there were a special measurement rate where the correlation length became infinite, the area-law-at-any-rate conclusion would fail.

Editorial extensions

If this is right

  • At any finite measurement rate 1/τ, the steady-state entanglement entropy in the thermodynamic limit follows an area law rather than a volume law.
  • The apparent logarithmic dependence of the stationary entropy on subsystem size is a finite-size effect that disappears once the subsystem length exceeds the correlation length ξ(τ).
  • The early-time entanglement growth changes from linear to logarithmic as soon as any nonzero measurement rate is introduced.
  • The scaling function f(ℓ/τ) = S_ℓ/(ℓ ln 2) collapses data for all rates and subsystem sizes onto a single curve, with the large-x branch behaving as 1/x.
  • The area-law value itself depends on the measurement rate through ln ξ(τ), so heavier monitoring produces smaller stationary entanglement.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: if the area-law-at-any-rate conclusion holds, then what is often called a measurement-induced transition in this model is not a sharp thermodynamic phase transition but a smooth crossover controlled by an exponentially large correlation length.
  • Editorial inference: the variance of the entanglement entropy, whose maximum grows linearly with subsystem size, may be a more sensitive diagnostic than the mean entropy for locating finite-size crossovers in monitored free-fermion systems.
  • Editorial inference: the result suggests that any nonzero density-measurement rate collapses volume-law entanglement in Gaussian fermionic dynamics, which could inform expectations for more interacting monitored systems where volume-law phases have been argued to be stable.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The manuscript reports a numerical study of entanglement dynamics in a one-dimensional free-fermion chain subject to random local projective density measurements. The authors observe that any finite measurement rate changes the early-time entanglement growth from linear to logarithmic, and they argue that the stationary entanglement entropy obeys an area law for all finite rates in the thermodynamic limit, with a prefactor proportional to ln ξ(τ), so that the apparent logarithmic scaling seen in finite-size simulations is a finite-size effect. The evidence is a scaling collapse S_ℓ/(ℓ ln2) = f(ℓ/τ) with f(x)→1 for x≪1 and f(x)→1/x for x≫1, presented in Sec. 3.2.

Significance. If the central claim is correct, it would rule out a measurement-induced entanglement phase transition in this exactly solvable free-fermion model and show that the volume-law phase is absent for any finite measurement rate, in contrast to some earlier numerical claims. The manuscript benefits from using Gaussian dynamics, which allows exact trajectory simulations, and it explicitly identifies the finite-size origin of intermediate logarithmic scaling. However, the significance is reduced by the fact that the paper is a conference proceedings that defers the analytical derivation to reference [30] and presents data from that paper without a self-contained justification.

major comments (3)
  1. [Section 3.2] The physical explanation based on an exponential correlation length ξ(τ) ∼ e^{ατ} is inconsistent with the scaling ansatz S_ℓ/(ℓ ln2) = f(ℓ/τ). If ξ(τ) grows exponentially, the crossover between volume-law and area-law behavior should occur at ℓ ∼ ξ(τ) ∼ e^{ατ}, so the natural scaling variable is ℓ/ξ(τ), not ℓ/τ; the stated limits f(x→0)=1 and f(x→∞)=1/x would then apply to the variable ℓ/ξ(τ). Conversely, if the ℓ/τ collapse in Fig. 3b is correct, the crossover occurs at ℓ ∼ τ, implying a linear correlation length, which contradicts the exponential growth stated in the same paragraph. The two statements cannot describe the same data, and the central thermodynamic-limit conclusion rests on this ansatz.
  2. [Section 3.2, Fig. 3a inset] The inset of Fig. 3a reports τ* ∼ ln ℓ for the inflection point, implying a crossover at τ ∼ ln ℓ. The scaling ansatz f(ℓ/τ) with crossover at ℓ/τ ∼ 1 implies τ* ∼ ℓ. These two behaviors are incompatible, and the paper does not explain how the collapse in Fig. 3b arises if τ* grows only logarithmically with ℓ. The numerical support for the central claim therefore needs either a revised scaling analysis or a derivation of the correct scaling variable.
  3. [Sections 1 and 3.2] The analytical arguments supporting the area-law conclusion are not presented in this manuscript but deferred to reference [30]. Since the central claim—'we numerically show the existence of a single area-law phase'—depends on the unproven large-x limit f(x)→1/x and on the thermodynamic extrapolation, the manuscript as written does not provide a self-contained case. The authors should either include the derivation or clearly state that the paper is a summary of [30] and restrict the claims accordingly.
minor comments (5)
  1. [Title] The title contains a typo: 'Measurments' should be 'Measurements'.
  2. [Section 2.2] The phrase 'the probability to have multiple measurement events at each time step dt is approximately zero' should be rephrased as 'the probability ... is negligible' or similar for clarity.
  3. [Section 3.1] The phrase 'the so called volume law' should be 'the so-called volume law'; similar hyphenation issues appear elsewhere (e.g., 'Zeno limite' should be 'Zeno limit').
  4. [Throughout] There are several spelling and grammar errors, including 'regim' (regime), 'appart' (apart), 'limite' (limit), and the inconsistent formatting of 'N ´eel'.
  5. [Section 4] The sentence 'the average of the asymptotic time entanglement entropy undergoes a transition from the volume-law to the area-law phase for any measurement rate' is confusing; it should clarify that the transition is only a crossover at finite ℓ and that in the thermodynamic limit the behavior is always area-law.

Circularity Check

2 steps flagged · score 6.0 of 10

The area-law-at-any-τ conclusion is read off the assumed f(ℓ/τ) scaling form imported from the authors' own Ref. [30].

  1. fitted input called prediction [Section 3.2, Stationary entanglement (text around Fig. 3b)]
    "As a consequence, in the thermodynamic limit ℓ ≫ 1, at any finite rate of measurements 1/τ the steady entanglement entropy follows an area-law ∝ ln ξ(τ). This is confirmed by analytical arguments based on the quasi-particles picture, see [30] for details, which predict that the steady entanglement entropy should scale as Sℓ(τ,t→∞)/(ℓ ln2) = f(ℓ/τ) where the scaling function f(x) has limits lim_{x≪1} f(x)=1 and lim_{x≫1} f(x)=1/x."

    The 'prediction' of an area law for every finite τ is read off the assumed large-x behavior f(x≫1)=1/x of the scaling function used to collapse the data in Fig. 3b. With that limit, S_ℓ ≈ ℓ ln2 · (τ/ℓ) = τ ln2, i.e. an area law; without it, the conclusion would not follow. Since the asymptotic form of f is an input (imported from [30] and imposed in the collapse) rather than a derived output of the present numerics, the claimed thermodynamic-limit result reduces to the scaling ansatz itself. The abstract's 'we numerically show the existence of a single area-law phase' is therefore a restatement of the fitted f-limit, not an independent numerical inference in this paper.

  2. self citation load bearing [Section 4, concluding paragraph]
    "This proceedings paper is based on the work [30] and all the figures presented here are extracted from that paper."

    Reference [30] is Coppola, Tirrito, Karevski and Collura (2022), i.e. the same authors as the present proceedings. The paper's own 'analytical arguments' for the scaling form f and for the absence of a volume-law phase are deferred to [30], and every numerical figure supporting those claims is taken from [30]. Thus the central area-law conclusion rests on a self-citation chain: the only cited derivation is the authors' prior paper, and the present paper adds no independent argument or new data. This is load-bearing, not incidental, because removing [30] leaves the scaling ansatz unsupported within the paper.

full rationale

The central claim — that in the thermodynamic limit the stationary entanglement entropy is area-law for every finite measurement rate, with no logarithmic phase — is not derived from first principles in this paper. The derivation chain is: (i) state an exponential correlation-length mechanism ξ(τ) ∼ e^{ατ}; (ii) import from the authors' earlier work [30] the scaling form Sℓ/(ℓ ln2) = f(ℓ/τ) with f(x≫1)=1/x; (iii) read off S ∼ τ from that limit, and call it an area law. Step (ii) carries all the weight, and it is an input rather than an output. The figures are explicitly extracted from [30], and the analytical support is also deferred to [30], so the paper is a report of the authors' own prior result rather than an independent derivation. The conclusion is therefore partly circular: the area-law-at-any-τ statement is equivalent to the assumed large-x tail of the scaling function. I do not score this as total circularity because the underlying numerics are real and the scaling collapse could in principle be a faithful empirical description; the paper simply does not establish that the collapse is not itself the conclusion. There is an additional internal-consistency problem in the same section: the text says the crossover is set by an exponentially growing ξ(τ) ∼ e^{ατ}, while the collapse variable is ℓ/τ, which would imply a linear-in-τ crossover; these two statements cannot both describe the same data unless an unexplained relation between τ and α is assumed. That conflict further weakens the derivation, but it is primarily a correctness concern rather than a separate circular step. Overall, the central 'prediction' reduces, by construction, to the assumed scaling ansatz and its [30]-sourced limits, so a score of 6 is appropriate: partial circularity, with the numerics retaining some independent empirical content.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new entities. It relies on a standard free-fermion model and a scaling ansatz for the steady-state entropy. The free parameters a(τ), b(τ), and α are fitted to numerical data, and the scaling form itself is an assumed functional dependence rather than a derived result.

free parameters (3)
  • a(τ)
    Slope of the transient logarithmic growth S_ℓ(t) ≈ a(τ) ln t + b(τ); a(τ) is read off the numerical curves as a function of measurement rate, not derived.
  • b(τ)
    Offset in the same logarithmic growth law; fitted from numerics.
  • α
    Exponent in the correlation length ξ(τ) ~ e^{ατ}; used to argue area-law for any finite τ; value not specified in this paper and presumably inferred from data.
assumptions (3)
  • standard math The monitored dynamics preserves Gaussianity for local density measurements
    Shown in Section 2.2 via a Baker-Campbell-Hausdorff argument; this is a technical result, not an assumption.
  • domain assumption The initial state is a Néel product state
    The numerics start from a product state; the transient behavior could depend on this choice.
  • ad hoc to paper The steady-state entropy obeys the scaling form S_ℓ/(ℓ ln2) = f(ℓ/τ) with specified limits
    This scaling ansatz is introduced to explain the data and is used to conclude area-law at any finite rate; it is stated without derivation in this paper.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Measurments-induced quantum phase transitions." pith.science (2026). https://pith.science/paper/2IQXP56Y

@misc{pith2026241206440,
  author       = {Pith},
  title        = {Pith review of: Measurments-induced quantum phase transitions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2IQXP56Y}},
  note         = {Machine review of arXiv:2412.06440}
}
read the original abstract

Dynamical phase transitions induced by local projective measurements have attracted a lot of attention in the past few years. It has been in particular argued that measurements may induce an abrupt change in the scaling law of the bipartite entanglement entropy. In this work we show that local projective measurements on a one-dimensional quadratic fermionic system induce a qualitative modification of the time growth of the entanglement entropy, changing from linear to logarithmic. However, in the stationary regime, the logarithmic behavior of the entanglement entropy does not survive in the thermodynamic limit and, for any finite value of the measurement rate, we numerically show the existence of a single area-law phase for the entanglement entropy. We give analytical arguments supporting our conclusions.

Figures

Figures reproduced from arXiv: 2412.06440 by the authors.

Figure 1
Figure 1. Evolution of the particle density after a sudden quench from a N [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Evolution of the averaged entanglement entropy for different rates 1/τ of measurements and subsystem sizes ℓ = 10,20,30,...,100 from bottom to top. The unitary case, τ = ∞, shows clearly the expected initial linear increase followed by the saturation toward the volume law ℓ ln2. Increasing the rate of measurements 1/τ, we observe from the numerics that the linear growth of the entanglement entropy suddenly changes t… view at source ↗
Figure 3
Figure 3. a) Stationary entanglement entropy versus [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: a) Fluctuations of the stationary entanglement entropy as a function of [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Nonstabilizerness in the unitary and monitored quantum dynamics of XXZ-staggered and SYK models

    quant-ph 2025-02 conditional novelty 6.0 of 10

    In monitored quantum-state-diffusion dynamics of XX, XXZ-staggered and SYK models, the steady-state nonstabilizerness is fit by a generalized Lorentzian and grows linearly with system size with no measurement-induced ...

Reference graph

Works this paper leans on

30 extracted references · 23 canonical work pages · cited by 1 Pith paper

  1. [30]

    Coppola, E

    M. Coppola, E. Tirrito, D. Karevski, M. Collura, Phys. Rev. B 105, 094303 (2022)

    work page 2022

  2. [1]

    Calabrese and J

    P. Calabrese and J. Cardy, J. Stat. Mech.: Theory Exp. (2005) P04010

    work page 2005

  3. [2]

    Amico, R

    L. Amico, R. Fazio, A. Osterloh, and V . Vedral, Rev. Mod. Phys. 80, 517 (2008)

    2008

  4. [3]

    Eisler, I

    V . Eisler, I. Peschel, J. Stat. Mech.: Theory Exp. P06005 (2007)

    work page 2007

  5. [4]

    Eisler, D.Karevski, T

    V . Eisler, D.Karevski, T. Platini, I Peschel, J. Stat. Mech.: Theory Exp. P01023 (2008)

    work page 2008

  6. [5]

    M Collura, D Karevski Physical review letters 104 (20), 200601 (2010)

    work page 2010

  7. [6]

    M Collura, D Karevski, Physical Review A 83 (2), 023603 (2011)

    work page 2011

  8. [7]

    S Scopa, D Karevski, Journal of Physics A: Mathematical and Theoretical 50 (42), 425301 (2017)

    work page 2017

Show all 30 references
  1. [8]

    S Scopa, J Unterberger, D Karevski, Journal of Physics A: Mathematical and Theoretical 51 (18), 185001 (2018)

    2018

  2. [9]

    Eisert, M

    J. Eisert, M. Cramer, M. B. Plenio, Rev. Mod. Phys. 82, 277 (2010)

    2010

  3. [10]

    Laflorencie, Physics Reports 646, 1 (2016)

    N. Laflorencie, Physics Reports 646, 1 (2016)

    2016

  4. [11]

    E. H. Lieb, D. W. Robinson, in Statistical mechanics (Springer, 1972) pp. 425-431

    1972

  5. [12]

    Alba, Physical Review B 97, 245135 (2018)

    V . Alba, Physical Review B 97, 245135 (2018)

    2018

  6. [13]

    Rigol, V

    M. Rigol, V . Dunjko, M. Olshanii, Nature 452, 854 (2008)

    2008

  7. [14]

    Ilievski, J

    E. Ilievski, J. De Nardis, B. Wouters, J.-S. Caux, F. H. L. Essler, T. Prosen, Physical Review Letters 115 (15), 157201 (2015)

    2015

  8. [15]

    Ilievski, M

    E. Ilievski, M. Medenjak, T. Prosen, L. Zadnik Journal of Statistical Mechanics: Theory and Experiment 2016 (6), 064008 (2016)

    2016

  9. [16]

    D. A. Abanin, E. Altman, I. Bloch, M. Serbyn, Reviews of Modern Physics 91, 021001 (2019)

    2019

  10. [17]

    Nahum, J

    A. Nahum, J. Ruhman, S. Vijay, J. Haah, Phys. Rev. X 7, 031016 (2017)

    2017

  11. [18]

    Skinner, J

    B. Skinner, J. Ruhman, and A. Nahum, Phys. Rev. X 9, 031009 (2019)

    2019

  12. [19]

    Y . Li, X. Chen, and M. P. A. Fisher, Phys. Rev. B 98, 205136 (2018)

    2018

  13. [20]

    A. Chan, R. M. Nandkishore, M. Pretko, and G. Smith, Phys. Rev. B 99, 224307 (2019)

    2019

  14. [21]

    Vasseur, A

    R. Vasseur, A. C. Potter, Y .-Z. You, A. W. W. Ludwig, Phys. Rev. B 100, 134203 (2019)

    2019

  15. [22]

    Y . Bao, S. Choi, E. Altman, Phys. Rev. B 101, 104301 (2020)

    2020

  16. [23]

    S. Choi, Y . Bao, X.-L. Qi, E. Altman, Phys. Rev. Lett. 125, 030505 (2020)

    2020

  17. [24]

    M. J. Gullans, D. A. Huse, Phys. Rev. Lett. 125, 070606 (2020)

    2020

  18. [25]

    Jian, Y .-Z

    C.-M. Jian, Y .-Z. You, R. Vasseur, A. W. W. Ludwig, Phys. Rev. B 101, 104302 (2020)

    2020

  19. [26]

    Zabalo, M

    A. Zabalo, M. J. Gullans, J. H. Wilson, S. Gopalakrishnan, D. A. Huse, J. H. Pixley, Phys. Rev. B 101, 060301 (2020)

    2020

  20. [27]

    X. Cao, A. Tilloy, and A. De Luca, SciPost Phys. 7, 024 (2019)

    2019

  21. [28]

    Alberton, M

    O. Alberton, M. Buchhold, and S. Diehl, Phys. Rev. Lett. 126, 170602 (2021)

    2021

  22. [29]

    Y . Fuji, Y . Ashida, Phys. Rev. B 102, 054302 (2020)

    2020

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.