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REVIEW 4 major objections 5 minor 44 references

Quantum Quenches from the Critical Point: Theory and Experimental Validation in a Trapped-Ion Quantum Simulator

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Starting a fast quantum quench from the critical point of the transverse-field Ising model makes the variance of the defect-pair number exactly linear in the quench depth, with a Gaussian distribution at leading order, as validated in a…

desk verdict The exact κ2=(L/16)εf result is clean and worth publishing; the experimental 'validation' needs error bars and a finite-rate check before the benchmark claim holds. read the letter →

arxiv 2507.01087 v1 pith:P7Q5TUUC submitted 2025-07-01 quant-ph

Chen-Xu Wang , András Grabarits , Jin-Ming Cui , Hua-Bi Zeng , Yun-Feng Huang , Chuan-Feng Li , Adolfo del Campo This is my paper
classification quant-ph
keywords quantumquenchtransverse-fieldIsingmodeldefectstatisticsfullcountingKibble-Zurekmechanismtrapped-ionsimulatorquench-depthscalingcumulants
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 attempts to establish that when a quantum system is quenched rapidly from its critical point, the statistics of the defects produced are controlled by the depth of the quench rather than by the quench rate. For the transverse-field Ising chain the authors derive exact fast-quench formulas showing that the average defect-pair number grows linearly in the quench depth $\epsilon_f$ with small corrections, the variance is exactly $\kappa_2 = (L/16)\epsilon_f$, and the third cumulant is linear with a quadratic suppression; consequently the defect-pair distribution is Gaussian at leading order. They report experimental confirmation using a trapped-ion simulator in which each momentum mode of an $N=100$ chain is emulated by a single qubit, starting near the critical point at $g_i=-1.01$ and quenching with $\tau_Q=0.07$. They also show that in the slow-driving regime all three cumulants follow a Kibble-Zurek-like $\tau_Q^{-1/2}$ scaling even when the quench starts near criticality. The paper's upshot is that quench-depth scaling becomes a precise, measurable benchmark for nonequilibrium quantum critical dynamics.

What carries the argument

The machinery is the momentum-space decomposition of the transverse-field Ising model into independent two-level systems via a Jordan-Wigner transformation and Fourier decomposition, with single-mode Hamiltonian $\hat H_k = \hat\varphi_k^\dagger[(g-\cos k)\sigma_z + \sin k\,\sigma_x]\hat\varphi_k$. The number of defect pairs is $\hat N = \sum_{k>0}\hat\gamma_k^\dagger(\epsilon_f)\hat\gamma_k(\epsilon_f)$, and each mode contributes a Bernoulli random variable with excitation probability $p_k$, the square of the overlap between the initial ground state at $g_i=-1$ and the final excited state at $g_f$. The argument evaluates these overlaps exactly, converts the sums over $k$ to integrals, and expands the resulting integrals in $\epsilon_f$; the variance integral collapses to $L\epsilon_f/16$ exactly. For slow driving, the same two-level decomposition and the scaling of the Schrödinger equation with $k^2\tau_Q$ motivate the numerically verified exponential ansatz $p_k \approx e^{-\pi k\sqrt{3\tau_Q}/2}$, from which the common $\tau_Q^{-1/2}$ scaling of all cumulants follows.

What would settle it

A decisive check is to measure the fourth cumulant $\kappa_4$ of the defect-pair distribution at fixed $N$ and several depths $\epsilon_f$: the Gaussian limiting claim requires $\kappa_4/\kappa_2^2 \to 0$ as $L$ grows, so a persistent size-independent nonzero ratio would falsify it; equivalently, inserting a variable hold time between quench and readout should leave $\kappa_2 = L\epsilon_f/16$ unchanged only in a closed system, so a systematic drift of $\kappa_2$ with hold time would rule out the interpretation.

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Extended reading notes

Core claim

The central discovery is a set of exact and approximate scaling laws for the cumulants of the defect-pair number in fast quenches that start from the quantum critical point of the transverse-field Ising model. Starting from the ground state at $g_c=-1$ and ending at depth $\epsilon_f = g_f + 1$, the mode-resolved excitation probabilities $p_k = |\langle ES_k(g_f)|GS_k(-1)\rangle|^2$ produce, in the integral approximation, $$\kappa_1 \approx \frac{L}{4\pi}\left[\epsilon_f + \frac{\pi-4}{8}\$epsilon_f^{2}$ - \frac{3\pi-10}{24}\$epsilon_f^{3}$ - \frac{3(5\pi-16)}{128}\$epsilon_f^{4}$ + \cdots\right],$$ $$\kappa_2 = \frac{L}{16}\epsilon_f,$$ $$\kappa_3 \approx \frac{L}{32\pi}\left[\epsilon_f - \frac{\pi-2}{128}\$epsilon_f^{2}$ - \frac{3\pi-10}{192}\$epsilon_f^{3}$ + \cdots\right].$$ Thus the leading-order distribution of defect pairs is Gaussian, with mean and variance both linear in $\epsilon_f$ and a skewness correction that grows more slowly. The paper reports that trapped-ion measurements with $N=100$, $g_i=-1.01$, and $\tau_Q=0.07$ match these predictions for the variance and the third cumulant, and match the average in the neighborhood of the critical point, while the slow-driving data follow a $\tau_Q^{-1/2}$ power law for all three cumulants.

Load-bearing premise

The load-bearing premise is that the trapped-ion qubit emulating each momentum mode, with $N=100$, $g_i=-1.01$, and $\tau_Q=0.07$, follows the same closed-system sudden-quench dynamics as the infinite-$N$ theory, so that no decoherence or detection bias distorts the measured $P(n)$.

Editorial extensions

If this is right

  • In the fast-quench limit from the critical point, the variance of the defect-pair number is exactly linear in the final quench depth with coefficient $L/16$, and the mean is linear up to small corrections, so measuring two cumulants at two depths fixes the prediction.
  • The defect-pair distribution approaches a Gaussian as the system size grows, with the third cumulant quantifying how slowly the skewness correction disappears.
  • In the slow-driving regime, all three cumulants follow the same $\tau_Q^{-1/2}$ Kibble-Zurek power law even when the quench starts near the critical point, with coefficients that differ from the large-$g_i$ case.
  • Defect pairs remain sub-Poissonian while total defect numbers are super-Poissonian, a distinction that can be tested by comparing the pair distribution with the defect distribution.
  • Quench-depth scalings of cumulants can serve as a quantitative benchmark for quantum simulators, since the full distribution $P(n)$ is directly measurable in the trapped-ion platform.

Reading between the lines

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

  • A natural extension the paper leaves implicit is to measure the fourth cumulant or the full distribution at larger $N$; the Gaussian leading-order claim predicts $\kappa_4/\kappa_2^2 \to 0$ with $L$, so a persistent nonzero value would reveal beyond-Gaussian or finite-size physics.
  • Because $\kappa_2 = (L/16)\epsilon_f$ is derived for a start exactly at $g_c=-1$, one could probe how the coefficient changes as the initial field is moved slightly off criticality ($g_i = -1+\delta$), quantifying how much 'critical' the initial state must be for the exact linearity to hold.
  • The same cumulant-ratio analysis could be applied to other integrable critical points, such as the XY model or long-range Ising chains, to see whether the Gaussian leading-order behavior and the $L/16$ coefficient are universal or model-specific.
  • If the scaling survives in larger systems, fast quenches from a critical point offer a benchmark that requires no adiabatic control: the simulator only needs to prepare a known ground state, quench rapidly, and read out the defect number.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript presents theory and trapped-ion experiments for the full counting statistics of defect pairs in the transverse-field Ising model after quantum quenches initiated near the quantum critical point. The central theoretical claims are exact and approximate expressions for the first three cumulants of the defect-pair number in the fast-quench limit: κ2 = (L/16) εf exactly, κ1 and κ3 given by low-order expansions in εf, and a Gaussian limiting distribution at leading order. The paper also proposes an exponential ansatz for slow-driving transition probabilities and reports Kibble-Zurek-like scaling of the cumulants. Experimental data from a 171Yb+ ion-trap simulator, with each momentum mode emulated by a single qubit and N = 100, are compared with the exact, approximate, and numerical results.

Significance. The exact closed form for κ2 and the explicit cumulant expansions are clean, parameter-free theoretical results that provide a useful benchmark for critical dynamics; the slow-driving exponential ansatz is falsifiable and the experimental approach of accessing defect-number cumulants in momentum space is well motivated. If the experimental validation is made non-circular and the finite-rate/off-critical corrections are quantified, the paper would establish quench-depth scaling as a practical benchmark for quantum simulators. At present, however, the experimental support is weakened by the calibration procedure and by missing uncertainty analysis, so the significance is conditional on the requested revisions.

major comments (4)
  1. [Universal defect scaling, Fig. 2 caption] The caption states that 'we use the average of the data in the fast quench region to fit the results of the numerical simulations,' and the text adds that 'The average is only recovered in the close neighborhood of the critical point.' This means the reported agreement in κ1 is a consistency check rather than an independent prediction, and it leaves open the possibility that the displayed agreement of κ2 and κ3 is inherited from the fitted absolute scale. Please report the raw, unscaled experimental and numerical curves, specify exactly which parameter(s) were adjusted in the fit, and demonstrate that the fitted scale accounts for the entire κ1 discrepancy before using the same numerical curves to validate κ2 and κ3.
  2. [Universal defect scaling, Eqs. (2)-(4)] The experimental protocol uses gi = -1.01 and τQ = 0.07, while the exact results assume a sudden quench from gi = -1. The comparison to numerical simulations with τQ = 0.01 does not establish that the actual experimental quench is inside the sudden limit; the exact finite-τQ solution of Ref. [24] makes this check directly available. Please provide a quantitative estimate of finite-rate and off-critical corrections at the experimental parameters, include them in the uncertainty budget, and report the number of experimental shots and error bars for the measured cumulants. Without this, the linear slope reported for κ2 cannot be attributed unambiguously to the exact law (3).
  3. [Universal defect scaling, Eq. (3) and Eq. (15)] Equation (3) is stated as exact, but the derivation in Eq. (15) replaces the discrete momentum sum by the continuum integral approximation. Please clarify whether κ2 = (L/16) εf is exact for finite N or only in the thermodynamic limit; if it is exact for finite N, provide a discrete-sum proof, and if it is a large-L result, quantify the finite-size correction for the N = 100 system used in the experiment and verify that it is smaller than the experimental scatter.
  4. [Slow-driving universality and Appendix] The exponential ansatz pk ≈ e^{-π k sqrt(3 τQ)/2} is central to the slow-driving cumulant predictions, but it is introduced as an expectation based on scaling and is verified only graphically in the Appendix. Please provide the fitting procedure, the extracted exponent with uncertainty, and a quantitative residual analysis, or explicitly label the resulting prefactors in κ1 ≈ L(6π^4 τQ)^(-1/2), κ2 ≈ κ1/2, κ3 ≈ κ1/3 as empirical rather than derived from the exact parabolic-cylinder solution.
minor comments (5)
  1. [Eq. (15)] The displayed derivation of κ2 contains internal inconsistencies: the first equality appears to have L/2 instead of L/8, and the substitution integrand shown as sqrt(1+t) sqrt(1-t) does not match the integral that is actually evaluated to π/(1-gf). The final result is plausible, but the displayed algebra should be corrected for readers to follow the derivation.
  2. [Slow-driving universality] The phrase 'for larger initial gi' should be clarified; since the experiments use gi = -1.01 near the critical point, the intended meaning is likely 'for initial parameters farther from criticality,' i.e., larger |gi|.
  3. [Reference [44]] Reference [44] appears as 'url will be inserted by publisher,' which is not usable in the arXiv version; please replace it with a working link to the Supplemental Material.
  4. [Sub-Poissonian/super-Poissonian terminology] The text says pair-number statistics is sub-Poissonian (κ2/κ1 < 1) and shortly after says defect-number cumulants are super-Poissonian (2κ2 > κ1). Please state explicitly that the first statement refers to defect pairs and the second to total defect number, so the apparent contradiction is resolved.
  5. [Universal defect scaling] The sentence 'the third cumulant exhibits a slower increase, consistent with stretched power-law behavior' is not quantified; if this is intended as a claim, please provide the fitted exponent and comparison range.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the fast-quench cumulant formulas are derived directly from the transverse-field Ising model, and the experimental average calibration and exponential ansatz are explicitly disclosed rather than concealed.

full rationale

The exact fast-quench results are derived self-containedly in the appendix from the TFIM single-mode overlaps: the excitation probabilities pk are computed from the ground and excited states, and the cumulants are then obtained by summing/integrating pk, pk(1–pk), and pk(1–pk)(1–2pk). In particular, κ2 = L/16 εf follows by evaluating the integral in Eq. (15), with no fitted parameter and no reliance on the paper's own prior results. The experimental comparison is transparent about its one calibration step: the Fig. 2 caption states that the experimental average was used to fit the numerical simulations, and the text explicitly concedes that "the average is only recovered in the close neighborhood of the critical point." Thus the first-cumulant agreement is not overclaimed as an independent prediction, and the claimed agreements for the variance and third cumulant are not the fitted observable. The slow-driving analysis uses an exponential ansatz pk ≈ e^{−πk√(3τQ/2)} that is explicitly described as "minimal numerical input" and validated numerically in the appendix; deriving cumulant scalings from this disclosed ansatz is an approximation, not a circular prediction. The self-citations ([20,24]) are not load-bearing: the paper rederives the needed exact expressions and the cited results are not used to forbid alternatives or to supply the central derivation. No step in the claimed derivation chain is equivalent to its inputs by construction.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central exact result rests on standard TFIM diagonalization and on treating momentum modes as independent Bernoulli sources of defect pairs. The slow-driving predictions add an exponential ansatz fitted to numerics. No new physical entities are introduced.

free parameters (2)
  • exponential suppression prefactor in slow-driving ansatz = sqrt(3) in pk ≈ e^{-π k sqrt(3 τQ)/2}
    The exponential form for slow-driving transition probabilities is introduced after 'minimal numerical input' and is validated only numerically, not derived from the Schrödinger equation.
  • experimental calibration via average defect number = unspecified scaling factor
    Fig. 2 caption states that the average of the data in the fast quench region is used to fit the numerical simulations, so the experimental mean cannot independently confirm the predicted linear scaling.
assumptions (5)
  • standard math Jordan-Wigner and Fourier transform map the transverse-field Ising Hamiltonian to independent two-level systems
    Standard diagonalization invoked in the 'TFQIM diagonalization' appendix.
  • domain assumption Defect pair number cumulants are sums of independent Bernoulli moments with probabilities pk
    Assumes decoupled momentum modes and independent defect generation; used throughout the cumulant derivations.
  • standard math In the thermodynamic limit, pk becomes continuous and the central limit theorem applies, yielding a Gaussian distribution
    Used to justify the Gaussian histograms and the leading-order behavior of cumulants.
  • ad hoc to paper Slow-driving transition probabilities take the exponential form pk ≈ e^{-π k sqrt(3 τQ)/2}
    Stated as revealed by minimal numerical input in 'Slow-driving universality'; no analytical derivation is provided.
  • domain assumption Time-dependent Schrödinger equation in the leading order depends on k^2 τQ, so pk inherits this scaling
    Used to argue KZ-like τQ^{-1/2} scaling for all cumulants; not explicitly proven.

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Cite this review

Pith. "Pith review of Quantum Quenches from the Critical Point: Theory and Experimental Validation in a Trapped-Ion Quantum Simulator." pith.science (2026). https://pith.science/paper/P7Q5TUUC

@misc{pith2026250701087,
  author       = {Pith},
  title        = {Pith review of: Quantum Quenches from the Critical Point: Theory and Experimental Validation in a Trapped-Ion Quantum Simulator},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P7Q5TUUC}},
  note         = {Machine review of arXiv:2507.01087}
}
read the original abstract

We investigate quantum quenches starting from a critical point and experimentally probe the associated defect statistics using a trapped-ion quantum simulator of the transverse-field Ising model. The cumulants of the defect number distribution exhibit universal scaling with quench depth, featuring Gaussian behavior at leading order and systematic subleading corrections. Our results are in excellent agreement with both exact and approximate theoretical predictions, establishing quench-depth scaling as a powerful and precise experimental benchmark for nonequilibrium quantum critical dynamics.

Figures

Figures reproduced from arXiv: 2507.01087 by the authors.

Figure 1
Figure 1. FIG. 1. Scheme of the experimental setup for controlling a [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. First three defect pair cumulants as a function of the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Histograms of the defect pair number in sudden [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Kibble-Zurek power-law scaling for the first three [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Excitation probabilities up to second order in [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. First three cumulants as a function of the quench depth. A precise agreement is found for the second-order [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Excitation probabilities in the slow driving limit for different values of [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Cumulant ratios of defect numbers by experimental results, numerical simulations, and analytical formulas. In all three [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Defect number cumulant ratios with varying driving time and for [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]

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Works this paper leans on

44 extracted references · 33 canonical work pages

  1. [24]

    Grabarits, F

    A. Grabarits, F. Balducci, and A. del Campo, Driving a quantum phase transition at an arbitrary rate: Exact solution of the transverse-field ising model, Phys. Rev. A 111, 042207 (2025)

    2025

  2. [1]

    Sachdev, Quantum Phase Transitions , 2nd ed

    S. Sachdev, Quantum Phase Transitions , 2nd ed. (Cam- bridge University Press, 2011)

    2011

  3. [2]

    T. W. B. Kibble, Topology of cosmic domains and strings, Journal of Physics A: Mathematical and General 9, 1387 (1976)

    work page 1976

  4. [3]

    W. H. Zurek, Cosmological experiments in superfluid he- lium?, Nature 317, 505 (1985)

    work page 1985

  5. [4]

    Zurek, Cosmological experiments in condensed mat- ter systems, Physics Reports 276, 177 (1996)

    W. Zurek, Cosmological experiments in condensed mat- ter systems, Physics Reports 276, 177 (1996)

    work page 1996

  6. [5]

    del Campo and W

    A. del Campo and W. H. Zurek, Universality of phase transition dynamics: Topological defects from symmetry breaking, International Journal of Modern Physics A 29, 1430018 (2014)

    work page 2014

  7. [6]

    Damski, The simplest quantum model supporting the kibble-zurek mechanism of topological defect production: Landau-zener transitions from a new perspective, Phys

    B. Damski, The simplest quantum model supporting the kibble-zurek mechanism of topological defect production: Landau-zener transitions from a new perspective, Phys. Rev. Lett. 95, 035701 (2005)

    work page 2005

  8. [7]

    Dziarmaga, Dynamics of a quantum phase transition: Exact solution of the quantum ising model, Phys

    J. Dziarmaga, Dynamics of a quantum phase transition: Exact solution of the quantum ising model, Phys. Rev. Lett. 95, 245701 (2005)

    work page 2005

Show all 44 references
  1. [8]

    W. H. Zurek, U. Dorner, and P. Zoller, Dynamics of a quantum phase transition, Phys. Rev. Lett. 95, 105701 (2005)

    2005

  2. [9]

    Cui, Y.-F

    J.-M. Cui, Y.-F. Huang, Z. Wang, D.-Y. Cao, J. Wang, W.-M. Lv, L. Luo, A. del Campo, Y.-J. Han, C.-F. Li, and G.-C. Guo, Experimental trapped-ion quantum sim- ulation of the kibble-zurek dynamics in momentum space, Scientific Reports 6, 33381 (2016)

    2016

  3. [10]

    Gardas, J

    B. Gardas, J. Dziarmaga, W. H. Zurek, and M. Zwolak, Defects in quantum computers, Scientific Reports8, 4539 (2018)

    2018

  4. [11]

    Weinberg, M

    P. Weinberg, M. Tylutki, J. M. R¨ onkk¨ o, J. Westerholm, J. A. ˚Astr¨ om, P. Manninen, P. T¨ orm¨ a, and A. W. Sand- vik, Scaling and diabatic effects in quantum annealing with a d-wave device, Phys. Rev. Lett. 124, 090502 (2020)

    2020

  5. [12]

    J.-M. Cui, F. J. G´ omez-Ruiz, Y.-F. Huang, C.-F. Li, G.- C. Guo, and A. del Campo, Experimentally testing quan- tum critical dynamics beyond the kibble–zurek mecha- nism, Communications Physics 3, 44 (2020)

    2020

  6. [13]

    Bando, Y

    Y. Bando, Y. Susa, H. Oshiyama, N. Shibata, M. Ohzeki, F. J. G´ omez-Ruiz, D. A. Lidar, S. Suzuki, A. del Campo, and H. Nishimori, Probing the universality of topological defect formation in a quantum annealer: Kibble-zurek mechanism and beyond, Phys. Rev. Research 2, 033369 (2020)

    2020

  7. [14]

    A. D. King, S. Suzuki, J. Raymond, A. Zucca, T. Lant- ing, F. Altomare, A. J. Berkley, S. Ejtemaee, E. Hoskin- son, S. Huang, E. Ladizinsky, A. J. R. MacDonald, G. Marsden, T. Oh, G. Poulin-Lamarre, M. Reis, C. Rich, Y. Sato, J. D. Whittaker, J. Yao, R. Harris, D. A. Lidar, H....

    2022

  8. [15]

    Li, Y.-K

    B.-W. Li, Y.-K. Wu, Q.-X. Mei, R. Yao, W.-Q. Lian, M.- L. Cai, Y. Wang, B.-X. Qi, L. Yao, L. He, Z.-C. Zhou, and L.-M. Duan, Probing critical behavior of long-range transverse-field ising model through quantum kibble- zurek mechanism, PRX Quantum 4, 010302 (2023)

    2023

  9. [16]

    A. Ali, H. Xu, W. Bernoudy, A. Nocera, A. D. King, and A. Banerjee, Quantum quench dynamics of geomet- rically frustrated ising models, Nature Communications 15, 10756 (2024)

    2024

  10. [17]

    Miessen, D

    A. Miessen, D. J. Egger, I. Tavernelli, and G. Mazzola, Benchmarking digital quantum simulations above hun- dreds of qubits using quantum critical dynamics, PRX Quantum 5, 040320 (2024)

    2024

  11. [18]

    A. D. King, A. Nocera, M. M. Rams, J. Dziarmaga, R. Wiersema, W. Bernoudy, J. Raymond, N. Kaushal, N. Heinsdorf, R. Harris, K. Boothby, F. Altomare, M. Asad, A. J. Berkley, M. Boschnak, K. Chern, H. Christiani, S. Cibere, J. Connor, M. H. Dehn, R. Desh- pande, S. Ejtemaee, P. ...

    2025

  12. [19]

    Zhang, H

    T. Zhang, H. Wang, W. Zhang, Y. Wang, A. Du, Z. Li, Y. Wu, C. Li, J. Hu, H. Zhai, and W. Chen, Observa- tion of near-critical kibble-zurek scaling in rydberg atom arrays (2025), arXiv:2505.07930 [cond-mat.quant-gas]

    2025 arXiv

  13. [20]

    Zeng, C.-Y

    H.-B. Zeng, C.-Y. Xia, and A. del Campo, Universal breakdown of kibble-zurek scaling in fast quenches across 6 a phase transition, Phys. Rev. Lett. 130, 060402 (2023)

    2023

  14. [21]

    Xia, H.-B

    C.-Y. Xia, H.-B. Zeng, C.-M. Chen, and A. del Campo, Structural phase transition and its critical dynamics from holography, Phys. Rev. D 108, 026017 (2023)

    2023

  15. [22]

    Kou and P

    H.-C. Kou and P. Li, Varying quench dynamics in the transverse ising chain: The kibble-zurek, saturated, and presaturated regimes, Phys. Rev. B 108, 214307 (2023)

    2023

  16. [23]

    Xia, H.-B

    C.-Y. Xia, H.-B. Zeng, A. Grabarits, and A. del Campo, Kibble-zurek mechanism and beyond: Lessons from a holographic superfluid disk (2024), arXiv:2406.09433 [cond-mat.stat-mech]

    2024 arXiv

  17. [25]

    Ejtemaee and P

    S. Ejtemaee and P. C. Haljan, Spontaneous nucleation and dynamics of kink defects in zigzag arrays of trapped ions, Phys. Rev. A 87, 051401 (2013)

    2013

  18. [26]

    S. Ulm, J. Roßnagel, G. Jacob, C. Deg¨ unther, S. T. Dawkins, U. G. Poschinger, R. Nigmatullin, A. Retzker, M. B. Plenio, F. Schmidt-Kaler, and K. Singer, Observa- tion of the Kibble-Zurek scaling law for defect formation in ion crystals, Nat. Comm. 4, 2290 (2013)

    2013

  19. [27]

    K. Pyka, J. Keller, H. L. Partner, R. Nigmatullin, T. Burgermeister, D. M. Meier, K. Kuhlmann, A. Ret- zker, M. B. Plenio, W. H. Zurek, A. del Campo, and T. E. Mehlst¨ aubler, Topological defect formation and sponta- neous symmetry breaking in ion Coulomb crystals, Nat. Comm. ...

    2013

  20. [28]

    X. Rao, Y. Liu, M. Li, T. Liu, H. Zeng, and L. Luo, Verified universal breakdown of kibble-zurek scaling in fast quenches (2025), arXiv:2506.06841 [quant-ph]

    2025 arXiv

  21. [29]

    B. Ko, J. W. Park, and Y. Shin, Kibble–zurek univer- sality in a strongly interacting fermi superfluid, Nature Physics 15, 1227 (2019)

    2019

  22. [30]

    Donadello, S

    S. Donadello, S. Serafini, T. Bienaim´ e, F. Dalfovo, G. Lamporesi, and G. Ferrari, Creation and counting of defects in a temperature-quenched bose–einstein conden- sate, Phys. Rev. A 94, 023628 (2016)

    2016

  23. [31]

    J. Goo, Y. Lim, and Y. Shin, Defect saturation in a rapidly quenched bose gas, Phys. Rev. Lett. 127, 115701 (2021)

    2021

  24. [32]

    J. Goo, Y. Lee, Y. Lim, D. Bae, T. Rabga, and Y. Shin, Universal early coarsening of quenched bose gases, Phys. Rev. Lett. 128, 135701 (2022)

    2022

  25. [33]

    del Campo, G

    A. del Campo, G. De Chiara, G. Morigi, M. B. Ple- nio, and A. Retzker, Structural defects in ion chains by quenching the external potential: The inhomogeneous kibble-zurek mechanism, Phys. Rev. Lett. 105, 075701 (2010)

    2010

  26. [34]

    Chandran, A

    A. Chandran, A. Erez, S. S. Gubser, and S. L. Sondhi, Kibble-zurek problem: Universality and the scaling limit, Phys. Rev. B 86, 064304 (2012)

    2012

  27. [35]

    Suzuki, J

    S. Suzuki, J. Inoue, and B. Chakrabarti, Quantum Ising Phases and Transitions in Transverse Ising Models , Lec- ture Notes in Physics (Springer, 2012)

    2012

  28. [36]

    Dziarmaga, Dynamics of a quantum phase transition and relaxation to a steady state, Advances in Physics 59, 1063 (2010)

    J. Dziarmaga, Dynamics of a quantum phase transition and relaxation to a steady state, Advances in Physics 59, 1063 (2010)

    2010

  29. [37]

    Cincio, J

    L. Cincio, J. Dziarmaga, M. M. Rams, and W. H. Zurek, Entropy of entanglement and correlations induced by a quench: Dynamics of a quantum phase transition in the quantum ising model, Phys. Rev. A 75, 052321 (2007)

    2007

  30. [38]

    del Campo, Universal statistics of topological defects formed in a quantum phase transition, Phys

    A. del Campo, Universal statistics of topological defects formed in a quantum phase transition, Phys. Rev. Lett. 121, 200601 (2018)

    2018

  31. [39]

    Subires, F

    D. Subires, F. J. G´ omez-Ruiz, A. Ruiz-Garc ´ ıa, D. Alonso, and A. del Campo, Benchmarking quantum annealing dynamics: The spin-vector langevin model, Phys. Rev. Res. 4, 023104 (2022)

    2022

  32. [40]

    Gherardini, L

    S. Gherardini, L. Buffoni, and N. Defenu, Universal de- fects statistics with strong long-range interactions, Phys. Rev. Lett. 133, 113401 (2024)

    2024

  33. [41]

    O. Kiss, D. Teplitskiy, M. Grossi, and A. Mandarino, Statistics of topological defects across a phase transition in a digital superconducting quantum processor, Quan- tum Science and Technology 10, 035037 (2025)

    2025

  34. [42]

    Visuri, A

    A.-M. Visuri, A. G. Cadavid, B. A. Bhargava, S. V. Romero, A. Grabarits, P. Chandarana, E. Solano, A. del Campo, and N. N. Hegade, Digitized counterdiabatic quantum critical dynamics (2025), arXiv:2502.15100 [quant-ph]

    2025

  35. [43]

    Grabarits and A

    A. Grabarits and A. del Campo, Universal defect statis- tics in counterdiabatic quantum critical dynamics (2025), arXiv:2503.22212 [quant-ph]

    2025 arXiv

  36. [44]

    1 − cos k 2 (gf − cos k) − sin k sin k 2 2 1 + g2 f − 2gf cos k # . (14) Thus, summing up the individual variances results in κ2 ≈ L 2π Z π 0 dk 1 4

    url will be inserted by publisher, . 7 TFQIM diagonalization With periodic boundary conditions, ˆ σz 1 = ˆσz N +1, the TFQIM is translationally invariant and can be diago- nalized using standard techniques. By performing a Jordan-Wigner transformation and a subsequent Fourier-...

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