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REVIEW 4 major objections 5 minor 68 references

Observation of far-from-equilibrium scaling in the transient dynamics of 2D quantum magnets

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Four different two-dimensional lattice geometries show the same collective magnetization dynamics after a quantum quench once interactions are rescaled by a coordination-weighted strength.

desk verdict A four-lattice Rydberg experiment shows a plausible geometry-independent rescaling of transient magnetization dynamics; the frequency collapse is expected, the damping collapse is new but remains empirically and quantitatively under-supported. read the letter →

arxiv 2608.07211 v1 pith:VLLZPSCW submitted 2026-08-07 cond-mat.quant-gas quant-ph

Fabio Bensch , Umberto Borla , Federico Balducci , Philip Osterholz , Shuanghong Tang , Silpa Baburaj Sheela , Anushya Chandran , Roderich Moessner
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Jad C. Halimeh Christian Gro{ss}
This is my paper · ORCID
classification cond-mat.quant-gasquant-ph
keywords transverse-fieldIsingmodelRydbergatomarraysquantumquenchdynamicsfar-from-equilibriumscalingdynamicalcriticalpointmodesofteningdampingratecollapsetensor-networksimulations
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

The paper tries to establish that even in the transient, far-from-equilibrium regime of short-range interacting two-dimensional quantum magnets, where mean-field arguments are not expected to hold, a simple organizing principle emerges: one interaction scale, $U_0^*=\tilde n_c U_0$, governs the dominant collective dynamics after a global quench. By realizing the transverse-field Ising model in Rydberg-atom arrays with four different lattice geometries, the authors find that both the softened oscillation frequency and the fluctuation-induced damping rate collapse onto common curves once scaled by $U_0^*$. If correct, this gives a geometry-independent route to predicting transient dynamics in 2D quantum magnets and identifies where mean-field, semiclassical, and tensor-network descriptions each become necessary. The result matters because transient quantum dynamics in two dimensions is the regime least covered by equilibrium universality and hardest for controlled numerics.

What carries the argument

The central object is the coordination-number-weighted interaction strength $U_0^* = \tilde n_c U_0$, with $\tilde n_c = \sum_{i\neq i_0} r_{i,i_0}^{-6}$, which turns the geometry-dependent van der Waals couplings of each lattice into a single energy scale. Around it the paper builds a mean-field collective-spin picture in which the magnetization precesses in a field $\vec B=(-\Omega,0,-U_0^* M_z/2)$, equivalent to a particle in an effective quartic potential $V(M_z)$ whose shape is fixed by $\Omega/U_0^*$; the critical value $\Omega_{\rm crit}=U_0^*/4$ marks the crossover where the mode softens to zero frequency. A two-population extension with bulk and edge spins explains why strong local longitudinal fields do not break the collective frequency, while discrete truncated Wigner and tree-tensor-network simulations provide the fluctuating many-body descriptions against which the measured damping and correlations are compared.

What would settle it

Run the honeycomb and square quenches with filling fraction reduced from about 90% to about 70% while keeping $\tilde n_c$ fixed: if the $\gamma/U_0^*$ curve moves with vacancy density or boundary fraction while the $\omega/U_0^*$ curve does not, the single-scale collapse of the damping is falsified.

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Extended reading notes

Core claim

After suddenly switching on a transverse field in the two-dimensional transverse-field Ising model, the fully magnetized initial state relaxes through a decaying collective magnetization oscillation whose frequency softens to a minimum and whose damping rate reaches a maximum near the same transverse field. The paper reports that this entire response is controlled by a single interaction scale, the coordination-number-weighted interaction strength $U_0^*=\tilde n_c U_0$, which accounts for the van der Waals tail beyond nearest neighbours. When $\Omega$, $\omega$, and $\gamma$ are rescaled by $U_0^*$, data from honeycomb, square, kagome, and triangular arrays collapse onto common curves. The frequency collapse is reproduced by a mean-field collective-spin description, with the minimum near $\Omega/U_0^*\approx 0.3$ close to the mean-field critical value $1/4$; the damping collapse is beyond mean field, and the failure of the discrete truncated Wigner approximation in the interaction-dominated regime shows that correlated quantum fluctuations, captured by tree-tensor-network simulations, are responsible.

Load-bearing premise

The collapse of the damping rate assumes that a single number, the coordination-weighted interaction strength computed from the ideal infinite lattice, absorbs all geometry-dependent effects, so that vacancies, edge fields, and beam inhomogeneity contribute to $\gamma$ in the same way for every lattice.

Editorial extensions

If this is right

  • The position of the dynamical crossover in a 2D Rydberg Ising system is set by $U_0^*$, not by the bare nearest-neighbor coupling; the measured frequency minimum sits near $\Omega/U_0^* \approx 0.3$, close to the mean-field value $1/4$.
  • Larger arrays sharpen the mode softening, so finite-size broadening is a controllable, understood correction to the scaling behavior.
  • Mean-field theory remains quantitatively useful for the collective frequency on transient timescales even though the microscopic model is short-ranged and strongly interacting.
  • The observed collapse of the damping rate implies that correlated quantum fluctuations, not just local dephasing from inhomogeneities, carry the geometry-independent collective scaling.
  • Beyond the crossover, a discrete truncated Wigner description works; near and below it, only tensor-network simulations reproduce the measured damping and correlations.

Reading between the lines

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

  • Beyond the paper, the $U_0^*$ collapse of the damping rate is empirical rather than derived; a microscopic calculation of $\gamma$ from the correlated fluctuation spectrum would show whether the single scale is exact or only approximate.
  • If the scaling is universal, the same quench protocol applied to other short-range 2D lattices with different $\tilde n_c$ values, for example a brickwall lattice or arrays with deliberately varied vacancy fractions, should land on the same master curves, a test the paper does not perform.
  • The paper hints that the principle might extend to frustrated magnets and lattice gauge theories; testing a frustrated geometry on the same platform would show whether geometric frustration introduces a new scale or leaves the $U_0^*$ collapse intact.
  • One might expect the collapse to hold only within the transient window before thermalization; monitoring the same observables to longer times would map the boundary of the scaling regime.
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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 paper reports global quenches of the transverse-field Ising model realized in Rydberg-atom arrays on four two-dimensional lattices (honeycomb, square, kagome, triangular). The central observation is that the frequency and damping rate of the dominant magnetization oscillation, extracted from exponentially damped harmonic fits, show a mode softening and a damping maximum at a common rescaled transverse field, with both quantities collapsing across geometries after rescaling by the coordination-number-weighted interaction strength U0* = tilde-N_c U0. The frequency collapse is shown to follow from a mean-field collective-spin description, whereas the damping collapse is presented as an empirical finding supported by TTN simulations for the square lattice and by the claimed failure of DTWA in the interaction-dominated regime.

Significance. If supported by quantitative analysis, the manuscript would establish a simple organizing principle for transient dynamics in short-range interacting two-dimensional quantum magnets and would provide a valuable benchmark hierarchy of theoretical methods. The experimental effort is substantial: four lattice geometries, robustness of the collective frequency against edge and vacancy fields, direct measurements of magnetization variance and nearest-neighbor correlations, and TTN simulations that quantitatively reproduce the square-lattice data. The paper is also commendably transparent about its limitations, including the square-lattice interaction correction in Supplement A and the absence of a microscopic derivation of the damping scaling. These same limitations, however, currently prevent the central scaling claim from being fully established.

major comments (4)
  1. [Fig. 3d and §4] The damping-rate collapse is the most novel part of the central claim, but it is established only by visual inspection. No goodness-of-fit statistic, residual analysis, or propagation of the uncertainty in U0* is provided, and no alternative collapse variable (e.g., the nearest-neighbor coordination zU0 or the actual per-site interaction sum in the finite arrays) is tested. With only four curves that differ in size, vacancy configuration, and longitudinal-field offset, a quantitative collapse metric is essential. I request a reduced chi-square or equivalent test of the common-curve hypothesis, with uncertainties propagated from the fit parameters and from the U0 calibration, and a comparison against at least one competing scaling choice.
  2. [Supplement A and Fig. 3a,b,d] The square-lattice data are corrected by assuming U0' = 2π×1.75 MHz instead of the nominal U0 = 2π×1.7 MHz, attributed to a 0.5% (35 nm) difference in lattice spacing. This is a load-bearing assumption because the square lattice is one of the four points in both the frequency and damping collapses. The manuscript should report an independent calibration of d0 or demonstrate that the collapse is robust when the nominal U0 is used and when the correction is varied within its uncertainty. As written, the square-lattice agreement is conditional on an unverified parameter.
  3. [§2 and Fig. 3d] The damping collapse is presented as evidence that U0* controls fluctuation-induced damping, but no microscopic mechanism or model calculation is provided. The four geometries differ in average longitudinal field (h_z/U0 = 0.3, -0.15, 0.19, 0.06), vacancy fraction, and array size, and some of these differences are not fully negligible even after rescaling by U0*. The paper should show that gamma is insensitive to these confounding parameters, for example by varying h_z in a single geometry or by reporting the actual per-site interaction sums for the finite, partially filled arrays. Without such a control, the damping collapse remains a hypothesis rather than an established scaling law.
  4. [Fig. 3d and §4] The statement that 'DTWA fits fail in the interaction-dominated regime, where no data points are shown' needs an objective failure criterion. Without showing representative fitted traces and residuals, the reader cannot distinguish a genuine breakdown of the semiclassical approximation from a numerical artifact of the fitting procedure. This matters because the DTWA failure is used to argue that correlated quantum fluctuations drive the damping.
minor comments (5)
  1. [References] Reference [61] is incomplete; it lacks a title, journal, and year and should be completed before publication.
  2. [Notation] The notation tilde-N_c appears as 'eNc' in the compiled text; please ensure the tilde is rendered consistently to avoid confusion with Euler's number.
  3. [Fig. 3b inset] The bulk, edge, and corner post-selection should state the number of sites in each class or provide statistical uncertainties on the post-selected frequencies.
  4. [Abstract] The phrase 'they reveal' appears twice in the abstract; consider tightening the final sentences.
  5. [Supplement A] The sentence stating that a 0.5% lattice shift explains the 3% interaction shift is a consistency check rather than a measurement; this should be stated explicitly so that the reader does not interpret it as an independent calibration.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the claimed scaling is an empirical/MF-based check against a geometry-derived scale, not a fitted parameter renamed as a prediction.

full rationale

The scaling variable U0* = eNc U0 is not fitted to the collapse. The paper defines eNc from the lattice geometry alone: "we account for by weighting each neighbor of a site i0 with its interaction strength, eNc = sum r^-6", and U0 is the independently measured nearest-neighbor interaction strength. The same combination appears naturally in the mean-field equations (Supplement C: B = (-Omega,0,-U0 eNc/2 Mz)), so the frequency collapse is a parameter-free comparison of data with an analytic MF prediction. The MF critical value Omega_crit/U0* = 1/4 is stated before comparing with the measured minimum near 0.3; the minimum is not imposed by a fit. The damping-rate collapse is empirical and is not derived from a microscopic theory, which is the opposite of circularity: no collapse exponent, scale, or damping curve is fitted to force the collapse, and the paper explicitly presents the result as a surprise: "The latter observation is surprising and suggests that correlated quantum fluctuations scaling with the effective coordination number of the lattices are responsible for the damping." The DTWA and TTN computations are independent semiclassical and tensor-network benchmarks, not fits to the scaling claim. Self-citations (Refs. 36-38 and 50) concern the experimental platform and prior numerical/analytical studies of mode softening; the essential MF derivation is repeated in the present Supplement C, and no load-bearing uniqueness claim rests on a self-citation. The Supplement A correction U0' = 2 pi x 1.75 MHz for the square array is a small systematic calibration attributed to a 0.5% lattice-spacing shift, not a parameter fitted to the collapse. Concerns about vacancies, local fields, finite-size effects, and the absence of a goodness-of-fit statistic for the damping collapse are validity and robustness limitations, not circularity, and therefore do not raise the circularity score.

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

No new particles, mediators, forces, dimensions, or conserved quantities are introduced. The coordination-number-weighted interaction strength U0* is a composite scale derived from geometry and U0, not an invented entity.

free parameters (2)
  • α (bulk fraction in two-population MF model) = 0.4
    Supplement C uses α = 0.4 to illustrate the two-population mode softening and frequency locking; this matches roughly the fraction of bulk sites in the 10x10 array (0.42) but is a hand-chosen value, not measured per shot.
  • U0' (square-lattice interaction correction) = 2π × 1.75 MHz
    Supplement A proposes a 3% larger nearest-neighbor interaction to reconcile the square-lattice frequency offset, attributing it to a 0.5% lattice-spacing error. This is ad hoc and not used in the main collapse.
assumptions (5)
  • domain assumption The transient quench dynamics of the short-range 2D TFIM is adequately captured by a single collective spin in a mean-field field B = (−Ω, 0, h_z − U0 ñ_c M_z/2).
    Used to derive mode softening, the critical field Ωcrit = U0 ñ_c/4, and the frequency rescaling. The paper argues large detuning suppresses small-scale domains, but the assumption is not rigorously justified for short-range interactions.
  • domain assumption The fully magnetized initial state lies in the high-energy sector where antiferromagnetic frustration on triangular and kagome lattices plays no role.
    This justifies treating all four lattices on equal footing despite different frustration. Stated in the Hamiltonian section.
  • domain assumption Van der Waals interaction tails are fully encoded by a single effective coordination number ñ_c = Σ_{i≠i0} r^{-6}, and longitudinal fields are dominated by nearest neighbors.
    This defines the scaling variable U0* and the approximate cancellation condition Δ = N_c U0/2. It assumes the long-range tail does not introduce a second relevant scale.
  • domain assumption The magnetization traces are well described by M_z(t) = A e^{−γt} cos(ωt + φ) + C, and the fitted ω and γ are physically meaningful observables.
    The entire frequency and damping collapse is built on this functional form; near the crossover the oscillation is strongly damped and the form may be poorly constrained, though TTN fits use the same model.
  • domain assumption The TTN model, with vacancies, Gaussian beam inhomogeneity, and no free parameters beyond measured U0 and Ω, correctly reproduces the experimental Hamiltonian and dynamics.
    TTN agreement is used to validate the experiment and the interpretation of damping; if the model omitted a relevant decoherence process, the damping comparison could mislead.

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Cite this review

Pith. "Pith review of Observation of far-from-equilibrium scaling in the transient dynamics of 2D quantum magnets." pith.science (2026). https://pith.science/paper/VLLZPSCW

@misc{pith2026260807211,
  author       = {Pith},
  title        = {Pith review of: Observation of far-from-equilibrium scaling in the transient dynamics of 2D quantum magnets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VLLZPSCW}},
  note         = {Machine review of arXiv:2608.07211}
}
read the original abstract

The transient regime of far-from-equilibrium quantum many-body dynamics lacks the established organizing principles that universality and scaling provide in equilibrium. It is least understood for two-dimensional short-range interacting systems, where mean-field arguments are not expected to hold, controlled theoretical descriptions are few, and fluctuations are strong. Here we investigate the quench dynamics of the transverse-field Ising model using programmable Rydberg-atom arrays realizing honeycomb, square, kagome, and triangular lattices. Starting from a fully magnetized state, we observe a pronounced softening of the dominant collective magnetization oscillation accompanied by a maximum in the damping rate, signaling a crossover between interaction- and field-dominated transient dynamics. Even though the microscopic lattice geometries are different, both the oscillation frequencies and the damping rates collapse onto common curves after being rescaled by the coordination-number-weighted interaction strength. Our findings show that a mean-field description effectively reproduces the magnetization oscillations. The importance of correlated quantum fluctuations is underlined by the failure of the discrete truncated Wigner approximation to predict the damping for strong interactions, while tree-tensor-network simulations reproduce the dynamics accurately. These results reveal a robust scaling regime governing the transient dynamics of short-range interacting two-dimensional quantum magnets. They reveal that the dominant transient dynamics is governed by a simple collective description despite the presence of strong quantum fluctuations --- an important insight in the quest to uncover organizing principles in far-from-equilibrium quantum matter.

Figures

Figures reproduced from arXiv: 2608.07211 by the authors.

Figure 1
Figure 1. FIG. 1. Illustration of the experimental system and MF in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Post-quench magnetization dynamics of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Mode softening and damping. Colors indicate the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Fluctuations and correlations in the 10 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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Works this paper leans on

68 extracted references · 36 canonical work pages

  1. [1]

    Polkovnikov, K

    A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalat- tore, Colloquium: Nonequilibrium dynamics of closed in- teracting quantum systems, Rev. Mod. Phys.83, 863 (2011)

    2011

  2. [2]

    Eisert, M

    J. Eisert, M. Friesdorf, and C. Gogolin, Quantum many- body systems out of equilibrium, Nat. Phys.11, 124 (2015)

    2015

  3. [3]

    Gogolin and J

    C. Gogolin and J. Eisert, Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems, Rep. Prog. Phys.79, 056001 (2016)

    2016

  4. [4]

    D’Alessio, Y

    L. D’Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65, 239 (2016)

    2016

  5. [5]

    Ueda, Quantum equilibration, thermalization and prethermalization in ultracold atoms, Nat

    M. Ueda, Quantum equilibration, thermalization and prethermalization in ultracold atoms, Nat. Rev. Phys. 2, 669 (2020)

    2020

  6. [6]

    Or´ us, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Ann

    R. Or´ us, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Ann. Phys.349, 117 (2014)

    2014

  7. [7]

    J. I. Cirac, D. P´ erez-Garc ´ ıa, N. Schuch, and F. Ver- straete, Matrix product states and projected entangled pair states: Concepts, symmetries, theorems, Rev. Mod. Phys.93, 045003 (2021)

    2021

  8. [8]

    T. Mori, T. N. Ikeda, E. Kaminishi, and M. Ueda, Ther- malization and prethermalization in isolated quantum systems: a theoretical overview, J. Phys. B: At. Mol. Opt. Phys.51, 112001 (2018)

    2018

Show all 68 references
  1. [9]

    Monroe, W

    C. Monroe, W. C. Campbell, L.-M. Duan, Z.-X. Gong, A. V. Gorshkov, P. W. Hess, R. Islam, K. Kim, N. M. Linke, G. Pagano, P. Richerme, C. Senko, and N. Y. Yao, Programmable quantum simulations of spin systems with trapped ions, Rev. Mod. Phys.93, 025001 (2021)

    2021

  2. [10]

    Browaeys and T

    A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nat. Phys.16, 132 (2020)

    2020

  3. [11]

    T. I. Andersen, N. Astrakhantsev, A. H. Karamlou, J. Berndtsson, J. Motruk, A. Szasz, J. A. Gross, A. Schuckert, T. Westerhout, Y. Zhang, E. Forati, D. Rossi, B. Kobrin, A. D. Paolo, A. R. Klots, I. Droz- dov, V. Kurilovich, A. Petukhov, L. B. Ioffe, A. Elben, A. Rath, V. Vita...

    2025

  4. [12]

    R. A. Barankov and L. S. Levitov, Synchronization in the BCS Pairing Dynamics as a Critical Phenomenon, Phys. Rev. Lett.96, 230403 (2006)

    2006

  5. [13]

    E. A. Yuzbashyan and M. Dzero, Dynamical Vanishing of the Order Parameter in a Fermionic Condensate, Phys. Rev. Lett.96, 230404 (2006)

    2006

  6. [14]

    Sciolla and G

    B. Sciolla and G. Biroli, Quantum Quenches and Off-Equilibrium Dynamical Transition in the Infinite- Dimensional Bose-Hubbard Model, Phys. Rev. Lett.105, 220401 (2010)

    2010

  7. [15]

    Sciolla and G

    B. Sciolla and G. Biroli, Dynamical transitions and quan- tum quenches in mean-field models, J. Stat. Mech.2011, P11003 (2011)

    2011

  8. [16]

    Homrighausen, N

    I. Homrighausen, N. O. Abeling, V. Zauner-Stauber, and J. C. Halimeh, Anomalous dynamical phase in quantum spin chains with long-range interactions, Phys. Rev. B 96, 104436 (2017)

    2017

  9. [17]

    J. Lang, B. Frank, and J. C. Halimeh, Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field ising model, Phys. Rev. B97, 174401 (2018)

    2018

  10. [18]

    Marino, M

    J. Marino, M. Eckstein, M. S. Foster, and A. M. Rey, Dy- namical phase transitions in the collisionless pre-thermal states of isolated quantum systems: Theory and experi- ments, Rep. Prog. Phys.85, 116001 (2022)

    2022

  11. [19]

    Zibold, E

    T. Zibold, E. Nicklas, C. Gross, and M. K. Oberthaler, Classical bifurcation at the transition from rabi to joseph- son dynamics, Phys. Rev. Lett.105, 204101 (2010)

    2010

  12. [20]

    Klinder, H

    J. Klinder, H. Keßler, M. Wolke, L. Mathey, and A. Hem- merich, Dynamical phase transition in the open Dicke model, Proc. Natl. Acad. Sci.112, 3290 (2015)

    2015

  13. [21]

    Trenkwalder, G

    A. Trenkwalder, G. Spagnolli, G. Semeghini, S. Coop, 8 M. Landini, P. Castilho, L. Pezz` e, G. Modugno, M. In- guscio, A. Smerzi, and M. Fattori, Quantum phase transi- tions with parity-symmetry breaking and hysteresis, Nat. Phys.12, 826 (2016)

    2016

  14. [22]

    Zhang, G

    J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, Observation of a many-body dynamical phase transition with a 53- Qubit quantum simulator, Nature 551, 601 (2017)

    2017

  15. [23]

    Jurcevic, H

    P. Jurcevic, H. Shen, P. Hauke, C. Maier, T. Brydges, C. Hempel, B. Lanyon, M. Heyl, R. Blatt, and C. Roos, Direct observation of dynamical quantum phase transi- tions in an interacting many-body system, Phys. Rev. Lett.119, 080501 (2017)

    2017

  16. [24]

    Smale, P

    S. Smale, P. He, B. A. Olsen, K. G. Jackson, H. Sharum, S. Trotzky, J. Marino, A. M. Rey, and J. H. Thywissen, Observation of a Transition Between Dynamical Phases in a Quantum Degenerate Fermi Gas, Sci. Adv.5, eaax1568 (2019)

    2019

  17. [25]

    H.-X. Yang, T. Tian, Y.-B. Yang, L.-Y. Qiu, H.-Y. Liang, A.-J. Chu, C. B. Da˘ g, Y. Xu, Y. Liu, and L.-M. Duan, Observation of dynamical quantum phase transitions in a spinor condensate, Phys. Rev. A100, 013622 (2019)

    2019

  18. [26]

    J. A. Muniz, D. Barberena, R. J. Lewis-Swan, D. J. Young, J. R. K. Cline, A. M. Rey, and J. K. Thompson, Exploring dynamical phase transitions with cold atoms in an optical cavity, Nature580, 602 (2020)

    2020

  19. [27]

    Tian, H.-X

    T. Tian, H.-X. Yang, L.-Y. Qiu, H.-Y. Liang, Y.-B. Yang, Y. Xu, and L.-M. Duan, Observation of Dynamical Quan- tum Phase Transitions with Correspondence in an Ex- cited State Phase Diagram, Phys. Rev. Lett.124, 043001 (2020)

    2020

  20. [28]

    Xu, Z.-H

    K. Xu, Z.-H. Sun, W. Liu, Y.-R. Zhang, H. Li, H. Dong, W. Ren, P. Zhang, F. Nori, D. Zheng, H. Fan, and H. Wang, Probing dynamical phase transitions with a su- perconducting quantum simulator, Sci. Adv.6, eaba4935 (2020)

    2020

  21. [29]

    D. J. Young, A. Chu, E. Y. Song, D. Barberena, D. Well- nitz, Z. Niu, V. M. Sch¨ afer, R. J. Lewis-Swan, A. M. Rey, and J. K. Thompson, Observing dynamical phases of BCS superconductors in a cavity QED simulator, Na- ture625, 679 (2024)

    2024

  22. [30]

    Schuckert, O

    A. Schuckert, O. Katz, L. Feng, E. Crane, A. De, M. Hafezi, A. V. Gorshkov, and C. Monroe, Observation of a finite-energy phase transition in a one-dimensional quantum simulator, Nat. Phys.21, 374 (2025)

    2025

  23. [31]

    Champion, A

    E. Champion, A. Schwartz, M. A. Ijaz, X. Xu, S. Camp- bell, G. T. Landi, and M. S. Blok, Analog quantum simu- lation of the Lipkin-Meshkov-Glick model in a transmon qudit (2025), arXiv:2512.05237 [quant-ph]

    2025

  24. [32]

    Natale, A

    G. Natale, A. Baumg¨ artner, J. Stefaniak, D. Baur, S. Hertlein, D. Rivero, T. Esslinger, and T. Donner, Syn- chronization of Quasiparticle Excitations in a Quantum Gas with Cavity-Mediated Interactions, Phys. Rev. Lett. 136, 140401 (2026)

    2026

  25. [33]

    Bullock, S

    B. Bullock, S. R. Muleady, J. F. Lilieholm, Y. Zhang, A. Safavi-Naini, R. J. Lewis-Swan, J. J. Bollinger, A. M. Rey, and A. L. Carter, Quantum simulation of the Dicke model in a two-dimensional ion crystal: Chaos, quantum thermalization, and revivals (2026), arXiv:2602.06114 [...

    2026

  26. [34]

    J. O. Austin-Harris, P. Sigdel, C. Binegar, S. E. Begg, T. Bilitewski, and Y. Liu, Control of dynamical phase transitions and non-ergodic relaxation via spinor phases (2025), arXiv:2511.03720 [cond-mat.quant-gas]

    2025 arXiv

  27. [35]

    C. B. Da˘ g and K. Sun, Dynamical crossover in the transient quench dynamics of short-range transverse-field Ising models, Phys. Rev. B103, 214402 (2021)

    2021

  28. [36]

    Hashizume, J

    T. Hashizume, J. C. Halimeh, and I. P. McCulloch, Hy- brid infinite time-evolving block decimation algorithm for long-range multidimensional quantum many-body sys- tems, Phys. Rev. B102, 035115 (2020)

    2020

  29. [37]

    Hashizume, I

    T. Hashizume, I. P. McCulloch, and J. C. Halimeh, Dynamical phase transitions in the two-dimensional transverse-field Ising model, Phys. Rev. Res.4, 013250 (2022)

    2022

  30. [38]

    Balducci, A

    F. Balducci, A. Chandran, and R. Moessner, Symmetry Rebreaking in an Effective Theory of Quantum Coarsen- ing, Phys. Rev. Lett.136, 020402 (2026)

    2026

  31. [39]

    K. G. Wilson, Renormalization group and critical phe- nomena. i. renormalization group and the kadanoff scal- ing picture, Phys. Rev. B4, 3174 (1971)

    1971

  32. [40]

    M. E. Fisher, The renormalization group in the theory of critical behavior, Rev. Mod. Phys.46, 597 (1974)

    1974

  33. [41]

    A. A. Zvyagin, Dynamical quantum phase transitions (re- view article), Low Temperature Physics42, 971 (2016)

    2016

  34. [42]

    Berges, M

    J. Berges, M. P. Heller, A. Mazeliauskas, and R. Venu- gopalan, QCD thermalization: Ab initio approaches and interdisciplinary connections, Rev. Mod. Phys.93, 035003 (2021)

    2021

  35. [43]

    A. N. Mikheev, I. Siovitz, and T. Gasenzer, Universal dynamics and non-thermal fixed points in quantum fluids far from equilibrium, Eur. Phys. J. Spec. Top.232, 3393 (2023)

    2023

  36. [44]

    Manovitz, S

    T. Manovitz, S. H. Li, S. Ebadi, R. Samajdar, A. A. Geim, S. J. Evered, D. Bluvstein, H. Zhou, N. U. Koylu- oglu, J. Feldmeier, P. E. Dolgirev, N. Maskara, M. Kali- nowski, S. Sachdev, D. A. Huse, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Quantum coarsening and collective dy-...

    2025

  37. [45]

    Lienhard, S

    V. Lienhard, S. de L´ es´ eleuc, D. Barredo, T. Lahaye, A. Browaeys, M. Schuler, L.-P. Henry, and A. M. L¨ auchli, Observing the space- and time-dependent growth of cor- relations in dynamically tuned synthetic ising models with antiferromagnetic interactions, Phys. Rev. X8, 0...

    2018

  38. [46]

    Guardado-Sanchez, P

    E. Guardado-Sanchez, P. T. Brown, D. Mitra, T. De- vakul, D. A. Huse, P. Schauß, and W. S. Bakr, Probing the quench dynamics of antiferromagnetic correlations in a 2D quantum ising spin system, Phys. Rev. X8, 021069 (2018)

    2018

  39. [47]

    Keesling, A

    A. Keesling, A. Omran, H. Levine, H. Bernien, H. Pich- ler, S. Choi, R. Samajdar, S. Schwartz, P. Silvi, S. Sachdev, P. Zoller, M. Endres, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg sim- ulator, Nat...

    2019

  40. [48]

    Bornet, G

    G. Bornet, G. Emperauger, C. Chen, B. Ye, M. Block, M. Bintz, J. A. Boyd, D. Barredo, T. Comparin, F. Mezzacapo, T. Roscilde, T. Lahaye, N. Y. Yao, and A. Browaeys, Scalable spin squeezing in a dipolar Ryd- berg atom array, Nature621, 728 (2023)

    2023

  41. [49]

    Darbha, A

    S. Darbha, A. Khudorozhkov, P. L. S. Lopes, F. Liu, E. Rrapaj, J. Balewski, M. Hamdan, P. E. Dolgirev, A. Schuckert, K. Klymko, S.-T. Wang, M. D. Lukin, D. Camps, and M. Kornjaˇ ca, Probing emergent prether- mal dynamics and resonant melting on a programmable 9 quantum simulat...

    2025

  42. [50]

    Osterholz, F

    P. Osterholz, F. Bensch, S. Tang, S. B. Sheela, B. Sbierski, I. Lesanovsky, and C. Groß, Collective clus- ter nucleation dynamics in quantum magnets (2025), arXiv:2512.04656 [cond-mat]

    2025

  43. [51]

    Defenu, T

    N. Defenu, T. Donner, T. Macr ` ı, G. Pagano, S. Ruffo, and A. Trombettoni, Long-range interacting quantum systems, Rev. Mod. Phys.95, 035002 (2023)

    2023

  44. [52]

    Schachenmayer, A

    J. Schachenmayer, A. Pikovski, and A. M. Rey, Many- body quantum spin dynamics with monte carlo trajecto- ries on a discrete phase space, Phys. Rev. X5, 011022 (2015)

    2015

  45. [53]

    W. K. Wootters, A wigner-function formulation of finite- state quantum mechanics, Ann. Phys.176, 1 (1987)

    1987

  46. [54]

    W. K. Wootters, Picturing qubits in phase space (2003), arXiv:quant-ph/0306135 [quant-ph]

    2003 arXiv

  47. [55]

    Vovrosh, S

    J. Vovrosh, S. Juli` a-Farr´ e, W. Krinitsin, M. Kaicher, F. Hayes, E. Gottlob, A. Kshetrimayum, K. Bidzhiev, S. B. J¨ ager, M. Schmitt, J. Tindall, C. Dalyac, T. Mendes-Santos, and A. Dauphin, Simulating dynam- ics of the two-dimensional transverse-field ising model: A compar...

    2026

  48. [56]

    Tagliacozzo, G

    L. Tagliacozzo, G. Evenbly, and G. Vidal, Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law, Phys. Rev. B80, 235127 (2009)

    2009

  49. [57]

    V. Murg, F. Verstraete, O. Legeza, and R. M. Noack, Simulating strongly correlated quantum systems with tree tensor networks, Phys. Rev. B82, 205105 (2010)

    2010

  50. [58]

    Semeghini, H

    G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kali- nowski, R. Samajdar, A. Omran, S. Sachdev, A. Vish- wanath, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Prob- ing topological spin liquids on a programmable quantum simul...

    2021

  51. [59]

    J. C. Halimeh, M. Aidelsburger, F. Grusdt, P. Hauke, and B. Yang, Cold-atom quantum simulators of gauge theories, Nat. Phys.21, 25 (2025)

    2025

  52. [60]

    J. C. Halimeh, N. Mueller, J. Knolle, Z. Papi´ c, and Z. Davoudi, Quantum simulation of out-of-equilibrium dynamics in gauge theories (2025), arXiv:2509.03586 [quant-ph]

    2025 arXiv

  53. [61]

    Mendes-Santos, et al., Exploring the Relaxation Land- scape of a 2D Quantum Magnet on a 256-Qubit Proces- sor

    T. Mendes-Santos, et al., Exploring the Relaxation Land- scape of a 2D Quantum Magnet on a 256-Qubit Proces- sor

  54. [62]

    I. P. Omelyan, I. M. Mryglod, and R. Folk, Algorithm for molecular dynamics simulations of spin liquids, Phys. Rev. Lett.86, 898 (2001)

    2001

  55. [63]

    Baccari, D

    F. Baccari, D. Bacilieri, M. Ballarin, F. P. Barone, F. Campaioli, A. G. Catalano, G. Cataldi, M. Colombo, A. Coppi, A. Costantini, A. Datta, A. De Girolamo, D. Jaschke, S. B. Koˇ zi´ c, G. Magnifico, C. Mordini, S. Montangero, M. Menon, G. Mu˜ noz Men´ es, S. Notar- nicola, A...

    2026

  56. [64]

    In the latter regime, the dynam- ics depends crucially on the energy of the central maxi- mum of the potential

    the potential is characterized by a double-well structure. In the latter regime, the dynam- ics depends crucially on the energy of the central maxi- mum of the potential. If the quench energyE 0 lies below 11 the energy of the maximum, the magnetization oscillates within a sin...

  57. [65]

    The Pauli operators at each site ˆXi, ˆYi, ˆZi are re- placed with classical spinss x i , sy i , sz i

  58. [66]

    all-down

    The initial “all-down” state is sampled from the discrete Wigner function, yielding eithers i(0) = (1,−1,−1) ors i(0) = (−1,1,−1) independently for each site, with equal probability

  59. [67]

    The quantum evolution is replaced with the Hamil- tonian evolution of a family ofNtraj classical trajec- tories{{s x,y,z i,n (t)}N i=1}Ntraj n=1 , each evolving indepen- dently under the dynamics generated by (the clas- sical limit of) the quantum Hamiltonian in Eq. (1). A sec...

  60. [68]

    Notice that the spins are not normal- ized to have length 1, but all expectation values of Pauli operators will take values between−1 and +1, after the trajectory average is taken

    The expectation values of observables are com- puted with the rules ⟨ ˆXi(t)⟩ ≈ 1 Ntraj NtrajX n=1 sx i,n(t),(S5) and similarly for the other spin operators, and com- binations thereof (where commutation relations do not matter). Notice that the spins are not normal- ized to h...

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.