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arxiv: 2501.17606 · v3 · submitted 2025-01-29 · 🪐 quant-ph · cond-mat.stat-mech

Disappearance of measurement-induced phase transition in a quantum spin system for large sizes

Paranjoy Chaki , Protyush Nandi , Ujjwal Sen , Subinay Dasgupta This is my paper

Pith reviewed 2026-05-23 04:30 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mech
keywords measurement-induced phase transitiontransverse Ising chainglobal measurementssurvival probabilitythermodynamic limitentanglementparamagnetic ground state
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The pith

The measurement-induced transition seen at moderate sizes in this globally monitored Ising chain recedes to zero measurement time in the thermodynamic limit.

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

The authors consider a transverse Ising chain in which each discrete time step consists of unitary evolution for an interval τ followed by a global projective measurement that answers whether every spin points up. For chains of length around 26 they observe, through direct simulation of survival probability and two entanglement quantifiers, an apparent change in behavior near τ approximately 0.2 when the transverse field is set to one-half. They then obtain an exact recursion relation for the survival probability that remains tractable up to length 1000; the location of the apparent transition extracted from this recursion scales as one over the square root of system size. Consequently the finite-size critical value drifts toward zero as the chain length is taken to infinity. In addition the long-time decay of survival probability becomes logarithmic exclusively when the ground state lies in the paramagnetic regime.

Core claim

In the model of repeated global measurements on the transverse-field Ising chain, finite-size numerics locate a measurement-induced transition at finite τ_c, yet the recursion relation derived for the survival probability shows that this τ_c scales to zero with increasing L, implying that the transition disappears in the thermodynamic limit; logarithmic decay of the survival probability at large times appears only when the ground state is paramagnetic.

What carries the argument

The recursion relation for the survival probability obtained from the sequence of unitary evolution under the transverse Ising Hamiltonian and the global projective measurement that returns whether all spins are up.

If this is right

  • The critical measurement interval τ_c extracted from the survival probability scales proportionally to 1/√L and therefore reaches zero in the thermodynamic limit.
  • At long times the survival probability exhibits logarithmic decay precisely when the ground state of the Hamiltonian is paramagnetic and shows no such decay when the ground state is ferromagnetic.
  • Bipartite entanglement and the generalized geometric measure both register the apparent transition for moderate chain lengths around 26.
  • The protocol employs deterministic global measurements at every step rather than probabilistic local measurements.

Where Pith is reading between the lines

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

  • Global all-or-nothing measurements may fail to stabilize a finite-time transition once system size is taken to infinity, unlike many local-measurement protocols.
  • The distinction between paramagnetic and ferromagnetic ground states controlling the long-time decay suggests that the nature of the unmonitored dynamics continues to influence the monitored steady state even at large L.
  • The 1/√L scaling could be tested by examining the same recursion on open-boundary or disordered variants of the Ising chain.

Load-bearing premise

The recursion relation for survival probability remains quantitatively accurate for system sizes up to thousands of spins and correctly locates the apparent transition without further approximations.

What would settle it

Direct computation of the survival-probability decay for system sizes larger than 1000 that either continues to push the fitted τ_c toward zero following the 1/√L form or instead stabilizes at a nonzero value.

Figures

Figures reproduced from arXiv: 2501.17606 by Paranjoy Chaki, Protyush Nandi, Subinay Dasgupta, Ujjwal Sen.

Figure 2
Figure 2. Figure 2: FIG. 2: Behavior of height of the plateau region of [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Survival probability [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Entanglement behavior with system size [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Behavior of multipartite entanglement with time-step [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Survival probability at large system sizes : In [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
read the original abstract

Measurement-induced phase transitions are often studied in random quantum circuits, with local measurements performed with a certain probability. We present here a model where a global measurement is performed with certainty at every time-step of the measurement protocol. Each time step, therefore, consists of evolution under the transverse Ising Hamiltonian for a time $\tau$, followed by a measurement that provides a ``yes/no'' answer to the question, ``Are all spins up?''. The survival probability after $n$ time-steps is defined as the probability that the answer is ``no'' in all the $n$ time-steps. For various $\tau$ values, we compute the survival probability, entanglement in bipartition, and the generalized geometric measure, a genuine multiparty entanglement, for a chain of size $L \sim 26$, and identify a transition at $\tau_c \sim 0.2$ for field strength $h=1/2$. We then analytically derive a recursion relation that enables us to calculate the survival probability for system sizes up to 1000, which provides evidence of a scaling $\tau_c \sim 1/\sqrt{L}$. The transition at finite \(\tau_c\) for \(L \sim 28\) seems therefore to recede to \(\tau_c = 0\) in the thermodynamic limit. Additionally, at large time-steps, survival probability decays logarithmically only when the ground state of the Hamiltonian is paramagnetic. Such decay is not present when the ground state is ferromagnetic.

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 examines a transverse-field Ising chain subject to deterministic global measurements at each time step: unitary evolution for duration τ under the Hamiltonian, followed by a projective check for the all-up state. Survival probability is the probability of never obtaining the 'yes' outcome over n steps. For L≈26 the authors numerically compute survival probability, bipartite entanglement, and generalized geometric measure, locating an apparent transition at τ_c≈0.2 (h=1/2). They then derive an exact recursion for the survival probability that permits computation up to L=1000 and report that τ_c scales as 1/√L, implying disappearance of the transition in the thermodynamic limit. They additionally observe that long-time logarithmic decay of survival probability occurs only when the ground state is paramagnetic.

Significance. If the recursion is faithful, the work supplies an analytically tractable global-measurement protocol in which an apparent finite-size transition can be shown to recede to zero, contrasting with the persistent transitions found in local-measurement circuits. The ability to reach L=1000 via recursion and the phase-dependent long-time decay constitute concrete, falsifiable results that could guide further studies of measurement-induced criticality.

major comments (2)
  1. [Analytical derivation of the recursion relation] The central scaling claim τ_c∼1/√L (and its extrapolation to the thermodynamic limit) rests on the recursion remaining quantitatively accurate for L up to 1000. The manuscript must therefore contain an explicit side-by-side comparison, for L≤26 and several values of τ near 0.2, between the recursion-evaluated survival probability and the direct numerical results already presented; any systematic deviation would undermine the scaling extrapolation.
  2. [Large-system results and scaling analysis] The procedure used to locate τ_c from the recursion data at large L is not stated. Because entanglement and GGM are unavailable for L=1000, the transition point must be inferred from some feature of the survival probability alone (e.g., a change in decay exponent or a crossing condition). The precise criterion, together with error bars on the extracted τ_c(L), must be supplied before the 1/√L fit can be assessed.
minor comments (2)
  1. [Abstract and numerical-results section] The abstract states L∼26 while the text later refers to L∼28; a single consistent value (or explicit range) should be used throughout.
  2. [Introduction or model section] The field value h=1/2 is used for the reported τ_c but the phase diagram of the underlying Ising model is not recalled; a brief reminder of the paramagnetic/ferromagnetic boundary would help readers interpret the long-time decay claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address the two major points below and will incorporate the requested clarifications and comparisons into the revised manuscript.

read point-by-point responses

  1. Referee: [Analytical derivation of the recursion relation] The central scaling claim τ_c∼1/√L (and its extrapolation to the thermodynamic limit) rests on the recursion remaining quantitatively accurate for L up to 1000. The manuscript must therefore contain an explicit side-by-side comparison, for L≤26 and several values of τ near 0.2, between the recursion-evaluated survival probability and the direct numerical results already presented; any systematic deviation would undermine the scaling extrapolation.

    Authors: We agree that an explicit validation is required. The recursion is obtained by an exact analytical derivation: after each unitary evolution segment the global projector onto the all-up state is applied, and the survival amplitude satisfies a closed linear recurrence whose coefficients depend only on the overlap of the evolved state with the measured subspace. Because the relation is exact, the recursion-evaluated survival probability must coincide with the direct numerics for all L≤26. In the revised manuscript we will add a supplementary figure (or table) showing this side-by-side comparison for L=26 and several τ values around 0.2, confirming agreement to machine precision and thereby justifying the use of the recursion for the large-L scaling analysis. revision: yes

  2. Referee: [Large-system results and scaling analysis] The procedure used to locate τ_c from the recursion data at large L is not stated. Because entanglement and GGM are unavailable for L=1000, the transition point must be inferred from some feature of the survival probability alone (e.g., a change in decay exponent or a crossing condition). The precise criterion, together with error bars on the extracted τ_c(L), must be supplied before the 1/√L fit can be assessed.

    Authors: We acknowledge that the precise extraction protocol for τ_c(L) from the survival probability alone was not stated. For large L we identify τ_c as the value at which the long-time decay of the survival probability changes from exponential to logarithmic, the latter being the signature observed only when the underlying Hamiltonian ground state is paramagnetic. In the revision we will (i) state this criterion explicitly, (ii) describe how the decay regime is diagnosed (fitting window, exponent threshold, or functional-form test), and (iii) report error bars on each τ_c(L) obtained by varying the fitting parameters or threshold. With these additions the 1/√L scaling fit can be properly evaluated. revision: yes

Circularity Check

0 steps flagged

No significant circularity; recursion presented as independent analytical step

full rationale

The paper computes survival probability, entanglement, and GGM numerically for L~26 to locate τ_c~0.2, then states it analytically derives a recursion relation for survival probability up to L=1000 to extract the scaling τ_c~1/√L. No quoted equation or text shows the recursion being fitted to the same data, defined in terms of the target scaling, or justified only via self-citation; it is described as an independent derivation. The extrapolation to thermodynamic limit therefore rests on the (unverified here) accuracy of that analytical step rather than reducing to a self-referential construction, satisfying the criteria for a self-contained derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the recursion is presented as derived from the model definition.

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Reference graph

Works this paper leans on

85 extracted references · 85 canonical work pages · 1 internal anchor

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    The point where this transition occurs is perfectly realized from the curve of panel (b), where we have plotted dH dτ vs

    The transition occurs around τc = 0.2. The point where this transition occurs is perfectly realized from the curve of panel (b), where we have plotted dH dτ vs. τ for various system sizes, that is, L = 20, 22, 24, 26 at field h = 1 2. Here, the highest value to each curve corresponds to the transition point. repeat this procedure of unitary evolution, fol...

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    The dependence of critical point τc on system size and h is studied in FIG (3). It is observed that the dependence of τc on h decreases as the system size L increases. τc also moves towards smaller values as system size L increases. In FIG (4), the survival probability is studied at large n at h = 3 2 for different τ values. We can see that Rn decays in l...

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    stochastically attained GGM

    System size is L = 50. A logarithmic decay at large time-steps is observed, which is not present at h < 1. ground state of transverse field Ising model. III. BIP AR TITE ENT ANGLEMENT Bipartite entanglement refers to entanglement, a quan- tum correlation [59–61] between two subsystems (or par- ties) in a composite quantum system. Suppose that A and B are ...

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    1 2 X k log

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