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arxiv: 2606.05288 · v1 · pith:W777JSOAnew · submitted 2026-06-03 · 🪐 quant-ph · cond-mat.stat-mech· cond-mat.str-el

Emergent Self-Similar Quantum Revivals in Spiral Drives

Xin-Chi Zhou , Liang-Hong Mo , Hongzheng Zhao , Bastien Lapierre This is my paper

Pith reviewed 2026-06-28 05:43 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mechcond-mat.str-el
keywords self-similar quantum revivalsquasiperiodic drivingdynamical attractorSU(2) cocyclesnonequilibrium quantum matterprethermal regimespiral kicks
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The pith

Quasiperiodic spiral kicks in a many-body system generate self-similar quantum revivals from an emergent dynamical attractor that forces all momentum modes into identical closed orbits at nested times.

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

The paper shows that a driven quantum system returns close to its starting state at a nested hierarchy of times rather than at regular intervals. Both the overlap with the initial state and the entanglement entropy repeat this self-similar pattern. The pattern is produced by one attractor that pulls every momentum mode onto the same closed orbit at the revival times. The authors prove the attractor exists by mapping the drive to quasiperiodic SU(2) cocycles, and they note that entanglement between revivals can follow either volume-law or area-law scaling depending on the drive parameters.

Core claim

In a many-body system driven by quasiperiodic spiral kicks the system recurrently returns close to its initial state at a hierarchically nested sequence of times originating from an emergent dynamical attractor such that all momentum modes eventually fall into the same closed orbits at self-similar times, justified analytically via quasiperiodic SU(2) cocycles.

What carries the argument

The emergent dynamical attractor, identified via quasiperiodic SU(2) cocycles, that synchronizes all momentum modes into identical closed orbits at self-similar revival times.

If this is right

  • Fidelity and entanglement entropy both display the same self-similar temporal structure.
  • Entanglement scaling between consecutive revivals switches between volume law and area law when driving parameters are changed.
  • Integrability-breaking perturbations produce a long-lived prethermal regime whose lifetime is algebraically tunable before eventual heating.
  • Special momentum modes realize the attractor through a generalized spin-echo process.

Where Pith is reading between the lines

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

  • The attractor mechanism may generalize to other quasiperiodic drives whose Floquet operators lie in SU(2).
  • The tunable prethermal lifetime offers a route to control heating rates in periodically driven simulators.
  • Observation of the nested revival hierarchy would constitute direct evidence for the attractor without requiring full state tomography.

Load-bearing premise

An emergent dynamical attractor exists and pulls every momentum mode into the same closed orbit at the self-similar times under exact quasiperiodic driving.

What would settle it

Direct measurement of the predicted nested revival times in a quantum simulator realizing the spiral drive, or the absence of such times when the drive is exactly quasiperiodic and unperturbed.

Figures

Figures reproduced from arXiv: 2606.05288 by Bastien Lapierre, Hongzheng Zhao, Liang-Hong Mo, Xin-Chi Zhou.

Figure 1
Figure 1. Figure 1: (a) Circuit representation of the spiral drive introduced in Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Parametrically long-lived non-heating dynamics under ran [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Plot of Tr(MFn ), as defined in (4), shown as a function of the index n for Haar distributed SU(2) matrices P, with 2000 random samples. The averaged value of the trace is shown in blue, and each realization of P is shown as a gray curve. We numerically observe the convergence to the period-6 pattern for all realizations of P. In order to prove this analytically, we will make use of the theory of quasiperi… view at source ↗
Figure 5
Figure 5. Figure 5: Deviation of the structure factor from its initial value ex [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
read the original abstract

We uncover a distinct form of nonequilibrium temporal order: self-similar quantum revivals in a many-body system driven by quasiperiodic spiral kicks, where the system recurrently returns close to its initial state at a hierarchically nested sequence of times. We demonstrate that both the fidelity and entanglement entropy exhibit this self-similar temporal structure. It originates from an emergent dynamical attractor, which we identify, such that all momentum modes eventually fall into the same closed orbits at self-similar times. We analytically justify this behavior and show that, for special momentum modes, this attractor arises as a consequence of a generalized spin echo process, and more generally we prove its existence using quasiperiodic SU(2) cocycles. Interestingly, the dynamics between consecutive revivals supports either volume- or area-law entanglement scaling, tunable via the driving parameters. In the presence of integrability-breaking perturbations, the system eventually heats up, but a long-lived prethermal regime with algebraically tunable lifetime occurs before heating sets in. Our results establish self-similar quantum revivals as a new paradigm for nonequilibrium quantum matter and provide a realistic route for its observation in current quantum simulators.

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

0 major / 3 minor

Summary. The manuscript claims that a many-body system driven by quasiperiodic spiral kicks exhibits self-similar quantum revivals, in which the system returns close to its initial state at a hierarchically nested sequence of times. This structure arises from an emergent dynamical attractor that organizes all momentum modes into the same closed orbits at self-similar times; the attractor is identified numerically via fidelity and entanglement entropy and is analytically justified, for special modes via a generalized spin-echo process and in general via quasiperiodic SU(2) cocycles. The dynamics between revivals permits tunable volume- or area-law entanglement scaling, and integrability-breaking perturbations produce a long-lived prethermal regime with algebraically tunable lifetime before eventual heating.

Significance. If the analytical justification via cocycles holds without hidden parameters, the work identifies a new form of nonequilibrium temporal order and supplies a concrete, simulator-accessible route to its observation. The explicit construction of the attractor, the demonstration that all momentum modes collapse onto the same orbits, and the separation between the ideal attractor and the prethermal regime under perturbations are substantive strengths.

minor comments (3)
  1. The model Hamiltonian and the precise definition of the spiral-kick protocol should be stated explicitly in the main text (rather than deferred to an appendix) to allow immediate reproduction of the numerics.
  2. Figure captions for the fidelity and entanglement plots should indicate the driving parameters used and the precise times at which the nested revivals occur, to make the self-similar hierarchy visually unambiguous.
  3. A brief remark on the numerical convergence with system size or momentum discretization would strengthen the claim that the attractor organizes all modes.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary of our manuscript and for recommending minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation relies on external cocycle framework

full rationale

The central claim of an emergent dynamical attractor organizing momentum modes into closed orbits at self-similar times is justified analytically via quasiperiodic SU(2) cocycles, presented as an independent mathematical tool rather than a self-referential definition or fitted input. No load-bearing steps reduce by construction to the paper's own equations, parameters, or self-citations. The prethermal regime under perturbations is treated separately and does not create a definitional loop. This is a standard case of a self-contained derivation against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the mathematical properties of quasiperiodic SU(2) cocycles and the identification of the dynamical attractor; no explicit free parameters or invented entities are stated in the abstract beyond tunable driving parameters.

axioms (1)
  • standard math Properties of quasiperiodic SU(2) cocycles allow proof of closed orbits for all momentum modes at self-similar times
    Invoked to analytically justify the emergent attractor.
invented entities (1)
  • emergent dynamical attractor no independent evidence
    purpose: Organizes momentum modes into closed orbits producing self-similar revivals
    Identified as the origin of the observed structure but presented as emergent rather than postulated a priori.

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Works this paper leans on

84 extracted references · 5 canonical work pages · 2 internal anchors

  1. [1]

    Levine and P

    D. Levine and P. J. Steinhardt, Quasicrystals: A new class of ordered structures, Phys. Rev. Lett.53, 2477 (1984)

    1984

  2. [2]

    Shechtman, I

    D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Metallic phase with long-range orientational order and no translational symmetry, Phys. Rev. Lett.53, 1951 (1984)

    1951

  3. [3]

    Jagannathan, The fibonacci quasicrystal: Case study of hid- den dimensions and multifractality, Rev

    A. Jagannathan, The fibonacci quasicrystal: Case study of hid- den dimensions and multifractality, Rev. Mod. Phys.93, 045001 (2021)

    2021

  4. [4]

    Kohmoto, B

    M. Kohmoto, B. Sutherland, and C. Tang, Critical wave func- tions and a cantor-set spectrum of a one-dimensional quasicrys- tal model, Phys. Rev. B35, 1020 (1987)

    1987

  5. [5]

    Y . E. Kraus and O. Zilberberg, Quasiperiodicity and topology transcend dimensions, Nat. Phys.12, 624 (2016)

    2016

  6. [6]

    Y . Wang, C. Cheng, X.-J. Liu, and D. Yu, Many-body critical phase: Extended and nonthermal, Phys. Rev. Lett.126, 080602 (2021)

    2021

  7. [7]

    Gonçalves, B

    M. Gonçalves, B. Amorim, F. Riche, E. V . Castro, and P. Ribeiro, Incommensurability enabled quasi-fractal order in 1D narrow-band moiré systems, Nat. Phys.20, 1933 (2024)

    1933

  8. [8]

    Bukov, L

    M. Bukov, L. D’Alessio, and A. Polkovnikov, Universal high- frequency behavior of periodically driven systems: from dy- namical stabilization to Floquet engineering, Adv. Phys.64, 139 (2015)

    2015

  9. [9]

    Khemani, A

    V . Khemani, A. Lazarides, R. Moessner, and S. L. Sondhi, Phase structure of driven quantum systems, Phys. Rev. Lett. 116, 250401 (2016)

    2016

  10. [10]

    D. V . Else, B. Bauer, and C. Nayak, Floquet time crystals, Phys. Rev. Lett.117, 090402 (2016)

    2016

  11. [11]

    Moessner and S

    R. Moessner and S. L. Sondhi, Equilibration and order in quan- tum Floquet matter, Nat. Phys.13, 424 (2017). 6

    2017

  12. [12]

    Harper, R

    F. Harper, R. Roy, M. S. Rudner, and S. L. Sondhi, Topology and broken symmetry in Floquet systems, Annu. Rev. Condens. Matter Phys.11, 345 (2020)

    2020

  13. [13]

    Autti, V

    S. Autti, V . B. Eltsov, and G. E. V olovik, Observation of a time quasicrystal and its transition to a superfluid time crystal, Phys. Rev. Lett.120, 215301 (2018)

    2018

  14. [14]

    Flicker, Time quasilattices in dissipative dynamical systems, SciPost Phys.5, 001 (2018)

    F. Flicker, Time quasilattices in dissipative dynamical systems, SciPost Phys.5, 001 (2018)

    2018

  15. [15]

    Giergiel, A

    K. Giergiel, A. Kuro ´s, and K. Sacha, Discrete time quasicrys- tals, Phys. Rev. B99, 220303 (2019)

    2019

  16. [16]

    Pizzi, J

    A. Pizzi, J. Knolle, and A. Nunnenkamp, Period-n Discrete Time Crystals and Quasicrystals with Ultracold Bosons, Phys. Rev. Lett.123, 150601 (2019)

    2019

  17. [17]

    Chinzei and T

    K. Chinzei and T. N. Ikeda, Time crystals protected by Floquet dynamical symmetry in hubbard models, Phys. Rev. Lett.125, 060601 (2020)

    2020

  18. [18]

    P. T. Dumitrescu, R. Vasseur, and A. C. Potter, Logarithmically slow relaxation in quasiperiodically driven random spin chains, Phys. Rev. Lett.120, 070602 (2018)

    2018

  19. [19]

    H. Zhao, F. Mintert, and J. Knolle, Floquet time spirals and sta- ble discrete-time quasicrystals in quasiperiodically driven quan- tum many-body systems, Phys. Rev. B100, 134302 (2019)

    2019

  20. [20]

    D. V . Else, W. W. Ho, and P. T. Dumitrescu, Long-Lived Inter- acting Phases of Matter Protected by Multiple Time-Translation Symmetries in Quasiperiodically Driven Systems, Phys. Rev. X 10, 021032 (2020)

    2020

  21. [21]

    L. J. I. Moon, P. M. Schindler, Y . Sun, E. Druga, J. Knolle, R. Moessner, H. Zhao, M. Bukov, and A. Ajoy, Experimental observation of a time rondeau crystal, Nature Physics , 1 (2025)

    2025

  22. [22]

    G. He, B. Ye, R. Gong, C. Yao, Z. Liu, K. W. Murch, N. Y . Yao, and C. Zu, Experimental Realization of Discrete Time Qua- sicrystals, Phys. Rev. X15, 011055 (2025)

    2025

  23. [23]

    J. Fang, Q. Zhou, and X. Wen, Phase transitions in quasiperiod- ically driven quantum critical systems: Analytical results, Phys. Rev. B111, 094304 (2025)

    2025

  24. [24]

    Zhu, Z.-Y

    D.-Y . Zhu, Z.-Y . Zhang, Q.-F. Wang, Y . Ma, T.-Y . Han, C. Yu, Q.-Q. Fang, S.-Y . Shao, Q. Li, Y .-J. Wang, J. Zhang, H.-C. Chen, X. Liu, J.-D. Nan, Y .-M. Yin, L.-H. Zhang, G.-C. Guo, B. Liu, D.-S. Ding, and B.-S. Shi, Observation of discrete time quasicrystal in rydberg atomic gases, arXiv:2509.21248

    work page arXiv

  25. [25]

    L.-H. Mo, R. Moessner, and H. Zhao, Complex and tunable heating in conformal field theories with structured drives via classical ergodicity breaking, Phys. Rev. B112, 184304 (2025)

    2025

  26. [26]

    Schmid, Y

    H. Schmid, Y . Peng, G. Refael, and F. von Oppen, Self-Similar Phase Diagram of the Fibonacci-Driven Quantum Ising Model, Phys. Rev. Lett.134, 240404 (2025)

    2025

  27. [27]

    Dynamical self-dual criticality in Fibonacci-monitored quantum Ising chains

    F. Eckstein, H. Schmid, Q. Preiss, S. Trebst, F. von Oppen, and G.-Y . Zhu, Dynamical self-dual criticality in fibonacci- monitored quantum ising chains, arXiv:2605.24086

    work page internal anchor Pith review Pith/arXiv arXiv

  28. [28]

    D’Alessio and M

    L. D’Alessio and M. Rigol, Long-time behavior of isolated pe- riodically driven interacting lattice systems, Phys. Rev. X4, 041048 (2014)

    2014

  29. [29]

    Lazarides, A

    A. Lazarides, A. Das, and R. Moessner, Equilibrium states of generic quantum systems subject to periodic driving, Phys. Rev. E90, 012110 (2014)

    2014

  30. [30]

    Ponte, A

    P. Ponte, A. Chandran, Z. Papi ´c, and D. A. Abanin, Period- ically driven ergodic and many-body localized quantum sys- tems, Ann. Phys.353, 196 (2015)

    2015

  31. [31]

    D. A. Abanin, W. De Roeck, and F. Huveneers, Exponentially slow heating in periodically driven many-body systems, Phys. Rev. Lett.115, 256803 (2015)

    2015

  32. [32]

    T. Mori, T. Kuwahara, and K. Saito, Rigorous bound on energy absorption and generic relaxation in periodically driven quan- tum systems, Phys. Rev. Lett.116, 120401 (2016)

    2016

  33. [33]

    D. A. Abanin, W. De Roeck, W. W. Ho, and F. Huveneers, Effective hamiltonians, prethermalization, and slow energy ab- sorption in periodically driven many-body systems, Phys. Rev. B95, 014112 (2017)

    2017

  34. [34]

    Abanin, W

    D. Abanin, W. De Roeck, W. W. Ho, and F. Huveneers, A rig- orous theory of many-body prethermalization for periodically driven and closed quantum systems, Commun. Math. Phys. 354, 809 (2017)

    2017

  35. [35]

    D. V . Else, B. Bauer, and C. Nayak, Prethermal phases of matter protected by time-translation symmetry, Phys. Rev. X7, 011026 (2017)

    2017

  36. [36]

    Ponte, Z

    P. Ponte, Z. Papi ´c, F. Huveneers, and D. A. Abanin, Many- body localization in periodically driven systems, Phys. Rev. Lett.114, 140401 (2015)

    2015

  37. [37]

    Lazarides, A

    A. Lazarides, A. Das, and R. Moessner, Fate of many-body lo- calization under periodic driving, Phys. Rev. Lett.115, 030402 (2015)

    2015

  38. [38]

    D. A. Abanin, W. De Roeck, and F. Huveneers, Theory of many-body localization in periodically driven systems, Ann. Phys.372, 1 (2016)

    2016

  39. [39]

    C. W. von Keyserlingk, V . Khemani, and S. L. Sondhi, Absolute stability and spatiotemporal long-range order in Floquet sys- tems, Phys. Rev. B94, 085112 (2016)

    2016

  40. [40]

    Zhang, P

    J. Zhang, P. W. Hess, A. Kyprianidis, P. Becker, A. Lee, J. Smith, G. Pagano, I.-D. Potirniche, A. C. Potter, A. Vish- wanath, N. Y . Yao, and C. Monroe, Observation of a discrete time crystal, Nature543, 217 (2017)

    2017

  41. [41]

    S. Choi, J. Choi, R. Landig, G. Kucsko, H. Zhou, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, V . Khemani, C. von Key- serlingk, N. Y . Yao, E. Demler, and M. D. Lukin, Observation of discrete time-crystalline order in a disordered dipolar many- body system, Nature543, 221 (2017)

    2017

  42. [42]

    N. Y . Yao, A. C. Potter, I.-D. Potirniche, and A. Vishwanath, Discrete time crystals: Rigidity, criticality, and realizations, Phys. Rev. Lett.118, 030401 (2017)

    2017

  43. [43]

    D. M. Long, P. J. D. Crowley, and A. Chandran, Many-body lo- calization with quasiperiodic driving, Phys. Rev. B105, 144204 (2022)

    2022

  44. [44]

    M. P. Zaletel, M. Lukin, C. Monroe, C. Nayak, F. Wilczek, and N. Y . Yao, Colloquium: Quantum and classical discrete time crystals, Rev. Mod. Phys.95, 031001 (2023)

    2023

  45. [45]

    Nandy, A

    S. Nandy, A. Sen, and D. Sen, Aperiodically driven integrable systems and their emergent steady states, Phys. Rev. X7, 031034 (2017)

    2017

  46. [46]

    Peng and G

    Y . Peng and G. Refael, Time-quasiperiodic topological su- perconductors with majorana multiplexing, Phys. Rev. B98, 220509 (2018)

    2018

  47. [47]

    P. J. D. Crowley, I. Martin, and A. Chandran, Topological clas- sification of quasiperiodically driven quantum systems, Phys. Rev. B99, 064306 (2019)

    2019

  48. [48]

    Boyers, P

    E. Boyers, P. J. D. Crowley, A. Chandran, and A. O. Sushkov, Exploring 2D Synthetic Quantum Hall Physics with 7 a Quasiperiodically Driven Qubit, Phys. Rev. Lett.125, 160505 (2020)

    2020

  49. [49]

    P. J. D. Crowley, I. Martin, and A. Chandran, Half-Integer Quantized Topological Response in Quasiperiodically Driven Quantum Systems, Phys. Rev. Lett.125, 100601 (2020)

    2020

  50. [50]

    Lapierre, K

    B. Lapierre, K. Choo, A. Tiwari, C. Tauber, T. Neupert, and R. Chitra, Fine structure of heating in a quasiperiodically driven critical quantum system, Phys. Rev. Res.2, 033461 (2020)

    2020

  51. [51]

    D. M. Long, P. J. D. Crowley, and A. Chandran, Nonadiabatic topological energy pumps with quasiperiodic driving, Phys. Rev. Lett.126, 106805 (2021)

    2021

  52. [52]

    Pilatowsky-Cameo, S

    S. Pilatowsky-Cameo, S. Choi, and W. W. Ho, Critically slow hilbert-space ergodicity in quantum morphic drives, Phys. Rev. Lett.135, 140402 (2025)

    2025

  53. [53]

    J. Wu, C. Liu, D. Bulmash, and W. W. Ho, Geometric quantum drives and topological dynamical responses: hyperbolically- driven quantum systems and beyond, arXiv:2503.08242

    work page arXiv

  54. [54]

    Krikorian, Global density of reducible quasi-periodic cocy- cles on T x SU(2), Annals of Mathematics154, 269 (2001)

    R. Krikorian, Global density of reducible quasi-periodic cocy- cles on T x SU(2), Annals of Mathematics154, 269 (2001)

    2001

  55. [55]

    Avila and R

    A. Avila and R. Krikorian, Reducibility or nonuniform hy- perbolicity for quasiperiodic Schrödinger cocycles, Annals of Mathematics 2,164, 911 (2006)

    2006

  56. [56]

    Sutherland, Simple system with quasiperiodic dynamics: a spin in a magnetic field, Phys

    B. Sutherland, Simple system with quasiperiodic dynamics: a spin in a magnetic field, Phys. Rev. Lett.57, 770 (1986)

    1986

  57. [57]

    X. Wen, R. Fan, A. Vishwanath, and Y . Gu, Periodically, quasiperiodically, and randomly driven conformal field theo- ries, Phys. Rev. Res.3, 023044 (2021)

    2021

  58. [58]

    Pilatowsky-Cameo, C

    S. Pilatowsky-Cameo, C. B. Dag, W. W. Ho, and S. Choi, Com- plete hilbert-space ergodicity in quantum dynamics of general- ized fibonacci drives, Phys. Rev. Lett.131, 250401 (2023)

    2023

  59. [59]

    Lapierre, L.-H

    B. Lapierre, L.-H. Mo, and S. Ryu, Entanglement transitions in structured and random nonunitary gaussian circuits (2025), arXiv:2507.03768 [quant-ph]

    work page arXiv 2025

  60. [60]

    [61, 62]

    See more details in Supplementary material, which includes Refs. [61, 62]

  61. [61]

    Dreyer, M

    H. Dreyer, M. Bejan, and E. Granet, Quantum computing criti- cal exponents, Phys. Rev. A104, 062614 (2021)

    2021

  62. [62]

    Granet, C

    E. Granet, C. Zhang, and H. Dreyer, V olume-Law to Area- Law Entanglement Transition in a Nonunitary Periodic Gaus- sian Circuit, Phys. Rev. Lett.130, 230401 (2023)

    2023

  63. [63]

    We note that the set of reducible single frequency cocycles over SU(2) is dense [54], which justifies this assumption

  64. [64]

    Bianchi, L

    E. Bianchi, L. Hackl, and M. Kieburg, Page curve for fermionic gaussian states, Phys. Rev. B103, L241118 (2021)

    2021

  65. [65]

    Mori, Heating rates under fast periodic driving beyond linear response, Physical review letters128, 050604 (2022)

    T. Mori, Heating rates under fast periodic driving beyond linear response, Physical review letters128, 050604 (2022)

    2022

  66. [66]

    X. Mi, M. Ippoliti, C. Quintana, A. Greene, Z. Chen, J. Gross, F. Arute, K. Arya, J. Atalaya, R. Babbush, J. C. Bardin, J. Basso, A. Bengtsson, A. Bilmes, A. Bourassa, L. Brill, M. Broughton, B. B. Buckley, D. A. Buell, B. Burkett, N. Bush- nell, B. Chiaro, R. Collins, W. Courtney, D. Debroy, S. De- mura, A. R. Derk, A. Dunsworth, D. Eppens, C. Erickson, ...

    2021

  67. [67]

    Z.-H. Liu, Y . Liu, G.-H. Liang, C.-L. Deng, K. Chen, Y .-H. Shi, T.-M. Li, L. Zhang, B.-J. Chen, C.-P. Fang, D. Feng, X.-Y . Gu, Y . He, K. Huang, H. Li, H.-T. Liu, L. Li, Z.-Y . Mei, Z.-Y . Peng, J.-C. Song, M.-C. Wang, S.-L. Wang, Z. Wang, Y . Xiao, M. Xu, Y .-S. Xu, Y . Yan, Y .-H. Yu, W.-P. Yuan, J.-C. Zhang, J.- J. Zhao, K. Zhao, S.-Y . Zhou, Z.-A. ...

    2026

  68. [68]

    Experimental observation of exact quantum critical states

    W. Huang, X.-C. Zhou, L. Zhang, J. Zhang, Y . Zhou, B.- C. Yao, Z. Guo, P. Huang, Q. Li, Y . Liang, Y . Liu, J. Qiu, D. Sun, X. Sun, Z. Wang, C. Xie, Y . Xiong, X. Yang, J. Zhang, Z. Zhang, J. Chu, W. Guo, J. Jiang, X. Linpeng, W. Ren, Y . Yuan, J. Niu, Z. Tao, S. Liu, Y . Zhong, X.-J. Liu, and D. Yu, Experimental observation of exact quantum critical sta...

    work page internal anchor Pith review Pith/arXiv arXiv

  69. [69]

    Chertkov, J

    E. Chertkov, J. Bohnet, D. Francois, J. Gaebler, D. Gresh, A. Hankin, K. Lee, D. Hayes, B. Neyenhuis, R. Stutz, A. C. Pot- ter, and M. Foss-Feig, Holographic dynamics simulations with a trapped-ion quantum computer, Nature Physics18, 1074–1079 (2022)

    2022

  70. [70]

    Moses, C

    S. Moses, C. Baldwin, M. Allman, R. Ancona, L. As- carrunz, C. Barnes, J. Bartolotta, B. Bjork, P. Blanchard, M. Bohn, J. Bohnet, N. Brown, N. Burdick, W. Burton, S. Campbell, J. Campora, C. Carron, J. Chambers, J. Chan, Y . Chen, A. Chernoguzov, E. Chertkov, J. Colina, J. Curtis, R. Daniel, M. DeCross, D. Deen, C. Delaney, J. Dreiling, C. Ertsgaard, J. E...

    2023

  71. [71]

    Haghshenas, E

    R. Haghshenas, E. Chertkov, M. Mills, W. Kadow, S.-H. Lin, Y . H. Chen, C. Cade, I. Niesen, T. Beguši ´c, M. S. Rudolph, C. Cirstoiu, K. Hémery, C. Mc Keever, M. Lubasch, E. Granet, C. H. Baldwin, J. P. Bartolotta, M. Bohn, J. J. Burau, J. Cline, M. DeCross, J. M. Dreiling, C. Foltz, D. Francois, J. P. Gae- bler, C. N. Gilbreth, J. Gray, D. Gresh, A. Hall...

    2026

  72. [72]

    S. J. Evered, D. Bluvstein, M. Kalinowski, S. Ebadi, T. Manovitz, H. Zhou, S. H. Li, A. A. Geim, T. T. Wang, N. Maskara, H. Levine, G. Semeghini, M. Greiner, V . Vuleti´c, and M. D. Lukin, High-fidelity parallel entangling gates on a neutral-atom quantum computer, Nature622, 268–272 (2023)

    2023

  73. [73]

    Bluvstein, S

    D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter, J. P. Bonilla Ataides, N. Maskara, I. Cong, X. Gao, P. Sales Rodriguez, T. Karolyshyn, G. Semeghini, M. J. Gul- lans, M. Greiner, V . Vuleti´c, and M. D. Lukin, Logical quan- tum processor based on reconfigurable atom arrays, Nature626,...

    2023

  74. [74]

    Manovitz, S

    T. Manovitz, S. H. Li, S. Ebadi, R. Samajdar, A. A. Geim, S. J. Evered, D. Bluvstein, H. Zhou, N. U. Koyluoglu, J. Feldmeier, P. E. Dolgirev, N. Maskara, M. Kalinowski, S. Sachdev, D. A. Huse, M. Greiner, V . Vuleti´c, and M. D. Lukin, Quantum coars- ening and collective dynamics on a programmable simulator, Nature638, 86–92 (2025). [75]⌈x⌉and⌊x⌋denote th...

    2025

  75. [75]

    Plugging these definitions into (13) leads to the first constraint u(x+φ) =−u(x),(14) 9 which implies thatu(x)≡0

    =−A(x);(12) introducingK(x) =B x+ 1 2 −1 B(x), this condition is equivalent to K(x+φ) =−CK(x)C −1.(13) Up to conjugacy,C=diag(e iβ, e−iβ), andK(x) = u(x)v(x) −¯v(x) ¯u(x) . Plugging these definitions into (13) leads to the first constraint u(x+φ) =−u(x),(14) 9 which implies thatu(x)≡0. Indeed, asφis irrational, it- erating (14) leads to a dense subset of ...

  76. [76]

    Moreover, we know thatKis off-diagonal, such that K(x) −1 =−K(x), soK(x+ 1

    = K(x) −1. Moreover, we know thatKis off-diagonal, such that K(x) −1 =−K(x), soK(x+ 1

  77. [77]

    Emergent Self-Similar Quantum Revivals in Spiral Drives

    =−K(x). This implies that kis odd, ase πik =−1. We conclude that Tr(CFn) = 2 cos(−πFn 2 +πkF nφ),(17) which, using Binet’s identity, converges towards Tr(CFn)→2 cos(− πFn 2 +πkF n−1),(18) and using thatk∈2Z+1, it is straightforward to conclude that Tr(CFn)converges to the values{0,0,2,0,0,−2}depending onnmod(6). We thus conclude that at stepsF 3n,A F3n(x)...

    2026

  78. [78]

    In Appendix S-1, we review the Gaussian-state formalism used to compute the time evolution of observables

  79. [79]

    In Appendix S-2, we prove convergence to the period-6 cycle, both in special cases and through perturbative arguments

  80. [80]

    In Appendix S-3, we demonstrate the emergence of revivals for spiral drives defined by different irrational numbers

Showing first 80 references.