Pith. sign in

REVIEW 2 major objections 1 minor 22 references

The uniform spacing of scar towers in the PXP model produces quadratic growth of the quantum Fisher information under resonant AC driving.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · grok-4.3

2026-06-28 00:32 UTC pith:RSBMWI2D

load-bearing objection Resonant driving on the PXP scar tower produces quadratic QFI growth for AC sensing via a single-tower approximation, with staggered magnetization showing better scaling than uniform. the 2 major comments →

arxiv 2606.06611 v1 pith:RSBMWI2D submitted 2026-06-04 quant-ph cond-mat.othercond-mat.stat-mech

Sensing ac fields with quantum many-body scars

Matheus Fibger , Andrei Tsypilnikov , Thiago R. de Oliveira , Fernando Iemini This is my paper
classification quant-ph cond-mat.othercond-mat.stat-mech
keywords quantum many-body scarsPXP modelquantum Fisher informationAC field sensingquantum metrologyresonant drivingweak ergodicity breaking
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 investigates whether the structured energy levels inside quantum many-body scars can be harnessed to sense the strength of a weak alternating field. It shows that the scar tower's roughly constant energy gaps let many states respond in phase when the drive frequency equals an integer multiple of the gap, producing a collective buildup that makes the quantum Fisher information grow quadratically with time for a prolonged interval. The authors compare probe operators and find that staggered magnetization yields a more favorable scaling with particle number than uniform magnetization. They also supply a reduced single-tower calculation that gives a closed-form expression for both the time dependence and the size dependence of the information.

Core claim

The approximately uniform energy spacing of the scar tower enables collective resonant processes when the driving frequency matches integer multiples of the scar gap, resulting in a quadratic-in-time growth of the QFI over an extended time window. Staggered magnetization leads to a more favorable growth of the QFI with system size than homogeneous magnetization. Frequency scanning and finite-size analysis characterize the scaling, and a single-tower approximation under resonant driving supplies a compact analytical expression for the time and system-size dependence of the QFI.

What carries the argument

The scar tower of the PXP model, whose approximately uniform energy spacing permits collective resonant responses to AC driving at multiples of the gap.

Load-bearing premise

The scar tower possesses approximately uniform energy spacing and the single-tower approximation remains valid for computing the QFI under resonant driving.

What would settle it

Numerical or experimental data showing that the quantum Fisher information grows only linearly with time, rather than quadratically, when the AC frequency is tuned to an integer multiple of the scar gap.

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

If this is right

  • The QFI grows quadratically with time for an extended window when the drive frequency matches multiples of the scar gap.
  • Staggered magnetization produces better scaling of the QFI with system size than homogeneous magnetization.
  • The single-tower approximation yields an analytical formula that reproduces the observed time and size dependence of the QFI.
  • Scanning the drive frequency isolates the resonance conditions that maximize the sensing window.

Where Pith is reading between the lines

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

  • The same resonant mechanism could be examined in other models known to host scar towers to test whether quadratic QFI growth is generic.
  • Direct measurement of the QFI in a quantum simulator of the PXP chain would provide a concrete test of the predicted scaling.
  • The approach suggests that any many-body system with an isolated tower of evenly spaced levels might offer similar metrological advantages under periodic driving.

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

2 major / 1 minor

Summary. The paper examines metrological applications of quantum many-body scars in the PXP model for estimating the amplitude of a weak AC field, using the quantum Fisher information (QFI) as the figure of merit. It claims that the scar tower's approximately uniform energy spacing permits collective resonant driving when the AC frequency matches integer multiples of the scar gap, producing quadratic-in-time QFI growth over an extended window. Different probe operators are compared, with staggered magnetization yielding more favorable system-size scaling than homogeneous magnetization. Frequency scans and finite-size numerics are presented, culminating in a single-tower approximation that supplies a compact analytical expression for the QFI time dependence and scaling.

Significance. If the central approximation holds, the work identifies a concrete mechanism by which structured non-ergodic dynamics can produce quadratic QFI growth and improved scaling in many-body sensors. The analytical expression derived from the scar tower supplies falsifiable predictions for time and size dependence that could guide experiments in Rydberg or other scarred platforms.

major comments (2)
  1. [single-tower approximation derivation] The single-tower approximation (invoked for the final analytical expression) projects the driven dynamics onto the scar tower and assumes off-tower matrix elements of both the probe and drive remain negligible throughout the quadratic window. No explicit bound on leakage amplitude or phase-error accumulation is supplied, nor is a direct comparison to full many-body evolution shown for the resonant frequencies and times at which quadratic growth is claimed. This step is load-bearing for both the quadratic growth and the reported system-size scaling.
  2. [finite-size analysis] Finite-size numerics are used to characterize QFI scaling with particle number, yet the manuscript does not report the range of system sizes, the precise fitting procedure, or error bars on the extracted exponents. Without these, it is difficult to assess whether the claimed advantage of staggered over homogeneous magnetization survives in the thermodynamic limit.
minor comments (1)
  1. [Notation] Notation for the scar gap and driving frequency should be introduced once and used consistently; the abstract refers to 'integer multiples of the scar gap' while the main text occasionally switches between Δ and ω_s without explicit cross-reference.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed review and valuable feedback on our manuscript. We address each major comment below, providing clarifications and indicating where revisions will be made to improve the presentation.

read point-by-point responses

  1. Referee: [single-tower approximation derivation] The single-tower approximation (invoked for the final analytical expression) projects the driven dynamics onto the scar tower and assumes off-tower matrix elements of both the probe and drive remain negligible throughout the quadratic window. No explicit bound on leakage amplitude or phase-error accumulation is supplied, nor is a direct comparison to full many-body evolution shown for the resonant frequencies and times at which quadratic growth is claimed. This step is load-bearing for both the quadratic growth and the reported system-size scaling.

    Authors: The single-tower approximation is motivated by the weak ergodicity breaking in the PXP model, where the scar states have exponentially small overlaps with the thermal bulk, leading to suppressed leakage under resonant driving. While we did not provide an explicit bound in the original manuscript, the quadratic growth is observed in our numerical simulations of the full dynamics for accessible system sizes, supporting the validity within the reported time window. To address this, we will include in the revision a direct comparison between the single-tower prediction and full many-body evolution for the largest accessible N, along with an estimate of the leakage rate derived from the scar state's fidelity decay. revision: yes

  2. Referee: [finite-size analysis] Finite-size numerics are used to characterize QFI scaling with particle number, yet the manuscript does not report the range of system sizes, the precise fitting procedure, or error bars on the extracted exponents. Without these, it is difficult to assess whether the claimed advantage of staggered over homogeneous magnetization survives in the thermodynamic limit.

    Authors: We agree that additional details on the finite-size scaling analysis are necessary. We will revise the manuscript to report the range of system sizes used in the numerics, describe the fitting procedure for the scaling exponents, and include error bars on the extracted values. This will facilitate assessment of whether the advantage of staggered over homogeneous magnetization holds in the thermodynamic limit. Our analysis suggests a favorable scaling, but we will add a note on the limitations of finite-size extrapolation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation follows from scar tower properties and explicit approximation

full rationale

The central claim of quadratic-in-time QFI growth is obtained by projecting onto the known approximately uniform scar tower spacing under resonant driving and invoking a single-tower approximation as an explicit modeling step. This does not reduce by construction to a fitted parameter or self-referential definition within the paper's equations. No load-bearing self-citations, ansatz smuggling, or renaming of known results are present in the provided derivation chain. The result remains independently falsifiable against the established PXP scar spectrum and full many-body numerics.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the PXP scar tower has approximately uniform spacing and that the single-tower model suffices for the QFI calculation; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption The PXP model possesses a tower of quantum many-body scars with approximately uniform energy spacing.
    Invoked to enable collective resonant processes at integer multiples of the scar gap.

pith-pipeline@v0.9.1-grok · 5721 in / 1332 out tokens · 32483 ms · 2026-06-28T00:32:07.687226+00:00 · methodology

0 comments
read the original abstract

Quantum many-body scars (MBS) exhibit weak ergodicity breaking and long-lived coherent dynamics within an otherwise thermal spectrum. We investigate their metrological properties using the quantum Fisher information (QFI), focusing on estimating the amplitude of a weak AC field in the PXP model. We show that the approximately uniform energy spacing of the scar tower enables collective resonant processes when the driving frequency matches integer multiples of the scar gap, resulting in a quadratic-in-time growth of the QFI over an extended time window. We analyze how the connectivity induced by different probe operators shapes sensing performance and demonstrate that staggered magnetization leads to a more favorable growth of the QFI with system size than homogeneous magnetization. Through frequency scanning and finite-size analysis, we characterize the scaling of the QFI with the number of particles. Finally, we develop a single-tower approximation under resonant driving, deriving a compact analytical expression that captures the time dependence and system-size scaling of the QFI. Our results establish how to leverage structured non-ergodic dynamics in quantum sensing protocols.

Figures

Figures reproduced from arXiv: 2606.06611 by Andrei Tsypilnikov, Fernando Iemini, Matheus Fibger, Thiago R. de Oliveira.

Figure 1
Figure 1. Figure 1: Fundamental phases of a quantum sensing pro [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: MBS tower.- Overlap of the PXP eigenstates {|Ei⟩} with the |Z2⟩ state for a chain with N = 20 spins. The tower structure, with its distinct layers, is clearly visible, with the highest-overlapping eigenstates spaced roughly equally in energy around the center of the spec￾trum. showing how to tune it to achieve quantum-enhanced per￾formance. Furthermore, we provide a semi-analytical ex￾pression for the QFI,… view at source ↗
Figure 3
Figure 3. Figure 3: The graph shows the connectivity (Oˆ) ℓℓ′ jj′ between the different scar states with N = 20 spins, considering either (a) a staggered field (Oˆstag), or (b) a homogeneous magnetization (Oˆz ). Thicker lines in the graph correspond to larger absolute values. Here, we show the connectivity among the first two main layers in the MBS tower spectrum. We see that the connections are significantly stronger among … view at source ↗
Figure 4
Figure 4. Figure 4: Finite-size scaling analysis for the connectiv [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Dynamics of the QFI at resonance frequency, [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Gaussian ansatz.- In the main panel, we show the initial state overlap with the dominant layer of the MBS spectral tower in a system with N = 20 spins. The distribution is Gaussian, with an amplitude that scales exponentially with system size (see inset panel b) and a variance that scales polynomially with N (see inset panel c). resonance are given by, Ri,i+2(ωtot, t) ≈ Rtot(ωtot, t) (20) = 1 2  e i(2∆E−ω… view at source ↗
Figure 7
Figure 7. Figure 7: Dynamics of the QFI off-resonantly, for dif [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

22 extracted references

  1. [1]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Quantum- enhanced measurements: beating the standard quantum limit, Science306, 1330 (2004)

    2004

  2. [2]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nature Photonics5, 222 (2011)

    2011

  3. [3]

    Pezze, A

    L. Pezze, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, Quantum metrology with nonclassical states of atomic ensembles, Reviews of Modern Physics 90, 035005 (2018)

    2018

  4. [4]

    S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, Improvement of frequency standards with quantum entanglement, Phys. Rev. Lett. 79, 3865 (1997)

    1997

  5. [5]

    B. M. Escher, R. L. de Matos Filho, and L. Davidovich, General framework for estimating the ultimate preci- sion limit in noisy quantum-enhanced metrology, Nature Physics7, 406 (2011)

    2011

  6. [6]

    Montenegro, C

    V. Montenegro, C. Mukhopadhyay, R. Yousefjani, S. Sarkar, U. Mishra, M. G. Paris, and A. Bayat, Quan- tum metrology and sensing with many-body systems, Physics Reports1134, 1 (2025)

    2025

  7. [7]

    Nandkishore and D

    R. Nandkishore and D. A. Huse, Many-body localiza- tion and thermalization in quantum statistical mechan- ics, Annual Review of Condensed Matter Physics6, 15 (2015)

    2015

  8. [8]

    D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Col- loquium: Many-body localization, thermalization, and entanglement, Reviews of Modern Physics91, 021001 (2019)

    2019

  9. [9]

    Serbyn, Z

    M. Serbyn, Z. Papi´ c, and D. A. Abanin, Quantum many- body scars and weak ergodicity breaking, Nature Physics 17, 675 (2021)

    2021

  10. [10]

    J. M. Deutsch, Quantum statistical mechanics in a closed system, Physical review a43, 2046 (1991)

    2046

  11. [11]

    Srednicki, Chaos and quantum thermalization, Phys- ical review e50, 888 (1994)

    M. Srednicki, Chaos and quantum thermalization, Phys- ical review e50, 888 (1994)

    1994

  12. [12]

    Rigol, V

    M. Rigol, V. Dunjko, and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems, Nature452, 854 (2008)

    2008

  13. [13]

    Dooley, S

    S. Dooley, S. Pappalardi, and J. Goold, Entanglement en- hanced metrology with quantum many-body scars, Phys- ical Review B107, 035123 (2023)

    2023

  14. [14]

    Dooley, Robust quantum sensing in strongly interact- ing systems with many-body scars, PRX Quantum2, 020330 (2021)

    S. Dooley, Robust quantum sensing in strongly interact- ing systems with many-body scars, PRX Quantum2, 020330 (2021)

    2021

  15. [15]

    H. e. a. Bernien, Probing many-body dynamics on a 51- atom quantum simulator, Nature551, 579 (2017)

    2017

  16. [16]

    C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papi´ c, Weak ergodicity breaking from quantum many-body scars, Nature Physics14, 745 (2018)

    2018

  17. [17]

    M. G. Paris, Quantum estimation for quantum technol- ogy, International Journal of Quantum Information7, 125 (2009)

    2009

  18. [18]

    Saad,Overview of Krylov subspace methods with ap- plications to control problems, Tech

    Y. Saad,Overview of Krylov subspace methods with ap- plications to control problems, Tech. Rep. (1989)

    1989

  19. [19]

    Kressner and C

    D. Kressner and C. Tobler, Krylov subspace methods for linear systems with tensor product structure, SIAM jour- nal on matrix analysis and applications31, 1688 (2010)

    2010

  20. [20]

    Demkowicz-Dobrza´ nski, J

    R. Demkowicz-Dobrza´ nski, J. Ko lody´ nski, and M. Gut ¸˘ a, The elusive heisenberg limit in quantum-enhanced metrology, Nature Communications3, 1063 (2012)

    2012

  21. [21]

    Tsypilnikov, M

    A. Tsypilnikov, M. Fibger, and F. Iemini, Exact analysis of ac sensors based on floquet time crystals, Phys. Rev. A113, 022620 (2026)

    2026

  22. [22]

    Iemini, R

    F. Iemini, R. Fazio, and A. Sanpera, Floquet time crys- tals as quantum sensors of ac fields, Phys. Rev. A109, L050203 (2024)

    2024