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To heat or not to heat: time crystallinity and finite-size effects in clean Floquet systems

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Pith's one-line read Homogeneous Floquet chains show no true discrete time crystal: the subharmonic response decays exponentially with system size, so observed clean-system signatures are finite-size effects.

desk verdict This paper settles the clean-DTC question with honest ED numerics and an analytic integrable-limit scaling: clean Floquet chains show exponentially long-lived finite-size time-crystalline signatures, but the response magnitude decays exponentially with system size, so no strict DTC survives in the thermodynamic limit. read the letter →

arxiv 2009.13527 v3 pith:VRJA6LTE submitted 2020-09-28 cond-mat.dis-nn quant-ph

Andrea Pizzi , Daniel Malz , Giuseppe De Tomasi , Johannes Knolle , Andreas Nunnenkamp This is my paper · ORCID
classification cond-mat.dis-nnquant-ph
keywords discretetimecrystalFloquetsystemsmany-bodylocalizationquantumscarssubharmonicresponsethermalizationfinite-sizeeffectscleanspinchains
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 examines whether disorder is necessary for a discrete time crystal (DTC) in a periodically driven spin chain. It argues that homogeneous, short-range-interacting Floquet systems produce the standard time-crystal diagnostics—an exponentially long subharmonic plateau and a spectral peak locked to frequency 1/2—but only as finite-size effects: the height of the plateau and the peak decay as $e^{-L/\lambda}$, so the response vanishes as $L\to\infty$. The origin is the $\pi$-pairing of just two scar-like eigenstates whose overlap with the initial condition decays exponentially, unlike many-body localized systems where all eigenstates pair and the response survives at infinite size. The paper concludes that only many-body localized systems realize a strict DTC, yet clean finite-size chains can still show clear time-crystalline signatures on exponentially long timescales, making them natural candidates for experiments.

What carries the argument

The load-bearing object is the $\pi$-pairing of Floquet eigenstates: two eigenstates of the unitary $U_F$ whose quasienergies differ by $\pi$, so that acting twice returns the state and the magnetization reverses every period. In the clean model, all of the subharmonic response comes from a single $\pi$-paired couple, approximated by $(|\Uparrow\rangle\pm|\Downarrow\rangle)/\sqrt{2}$, whose combined overlap with the initial condition falls as $[\cos(\theta/2)]^{2L}=e^{-L/\lambda}$; by contrast the MBL model $\pi$-pairs all eigenstates. This two-state mechanism plays the role of a quantum scar, and its exponential overlap decay is what turns the plateau and peak heights into exponentially suppressed quantities.

What would settle it

Compute the two largest eigenstate overlaps and the subharmonic plateau height in the clean model at system sizes beyond the point where the spectrum of $H_2$'s minibands merges; if either quantity stops following $e^{-L/\lambda}$ or tends to a positive constant as $L$ grows, the central claim fails.

Watch

Extended reading notes

Core claim

The paper's central claim is that the subharmonic, period-doubled response of a homogeneous Floquet spin chain is a finite-size effect. Under the two-step drive $U_F = e^{-iH_2/2} e^{-iH_1/2}$, both the subharmonicity plateau and the Fourier peak at $f=1/2$ are exponentially long-lived and robust to perturbations, so the usual diagnostics for time crystallinity are fulfilled at accessible sizes. However, careful scaling shows their magnitude decays exponentially with system size, $e^{-L/\lambda(\theta)}$, with $\lambda(\theta)=[-2\log(\cos(\theta/2))]^{-1}$ in the integrable limit and numerically large values (up to about 650) for small initial rotation $\theta$. The response is carried by exactly two $\pi$-paired eigenstates, approximately $(|\Uparrow\rangle\pm|\Downarrow\rangle)/\sqrt{2}$, whose combined overlap with the initial condition obeys the same exponential decay. In a many-body localized chain, all eigenstates are $\pi$-paired and the plateau height does not decay with $L$; therefore only MBL systems can satisfy the strict definition of a DTC, stable to perturbations and persistent to infinite times in the thermodynamic limit.

Load-bearing premise

The claim that no clean time crystal survives in the thermodynamic limit depends on extrapolating a small- or moderate-size exponential decay to $L\to\infty$; if the merging of the spectral bands at a larger critical size changes that trend, the subharmonic response could survive.

Editorial extensions

If this is right

  • For homogeneous Floquet spin chains, no strict discrete time crystal exists in the thermodynamic limit: the subharmonic response vanishes and the system heats to a featureless state on a timescale set by the integrability-breaking strength.
  • The standard diagnostics (exponential lifetime of the subharmonic plateau and a peak locked to frequency $1/2$) do not by themselves distinguish an MBL time crystal from a finite-size clean echo; one must also check how the plateau height scales with $L$.
  • For small initial rotations, the characteristic size $\lambda$ can reach hundreds of spins, so clean chains of experimentally realistic sizes can display crisp time-crystalline signatures for exponentially long times even though they are not true time crystals.
  • In many-body localized chains, the plateau height is essentially independent of system size, confirming that MBL systems remain the viable route to a strict Floquet time crystal.

Reading between the lines

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

  • Editorial inference: the same $e^{-L/\lambda}$ suppression should reappear in other reported clean time-crystal candidates (hard-core bosons, spinless fermions) if their analogous two-state overlaps were computed; the paper's own models are generic, but the transfer is not demonstrated there.
  • Editorial inference: if the merging of the spectral minibands at a critical size $L_c$ changes the scaling trend, the decay could turn into a crossover rather than a monotonic approach to zero; looking for that bend in larger numerics or simulators would test the thermodynamic-limit claim directly.
  • Editorial inference: interpolating disorder from zero to many-body-localized strength should continuously turn two-state $\pi$-pairing into full-spectrum $\pi$-pairing, which would tie the finite-size clean signatures to the MBL transition in a way the paper leaves open.
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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

3 major / 5 minor

Summary. This paper asks whether homogeneous (disorder-free) Floquet spin chains can realize a discrete time crystal (DTC). Using exact diagonalization of a clean and an MBL spin-1/2 chain, it studies two standard DTC diagnostics: the subharmonicity Z(t) and the subharmonic Fourier peak. In finite systems, both models show exponentially long-lived subharmonic plateaus; in the clean model, however, the plateau height and the spectral peak decay exponentially in system size with a scale lambda(theta), whereas in the MBL model they do not decay. The authors attribute the clean-model response to a single pi-paired pair of scar-like eigenstates approximately (|up arrow> +/- |down arrow>)/sqrt(2), and provide a parameter-free integrable-limit calculation giving the overlap decay [cos(theta/2)]^{2L}. They conclude that in the thermodynamic limit homogeneous systems heat and only MBL systems realize a strict DTC, while finite clean systems still exhibit crisp, exponentially long-lived time-crystalline signatures. The Supplementary Material extends the results to a different family of initial conditions and analyzes the level statistics of H2, noting a miniband structure that may affect the finite-size scaling.

Significance. If the conclusions hold, the paper clarifies a controversy: the standard DTC diagnostics can be fulfilled in clean finite-size systems, but the subharmonic response is exponentially suppressed with system size and therefore disappears in the thermodynamic limit. This is an important distinction from MBL DTCs and has direct implications for experiments on clean quantum simulators. The paper's strengths are the exact diagonalization data up to L=18 (21 for the H2 spectrum), the analytic parameter-free scaling in the integrable limit, the direct clean-vs-MBL comparison, and the honest discussion of the miniband caveat. The central negative thermodynamic-limit claim, however, relies on an extrapolation that is weakest for small theta, exactly the regime in which the response is longest-lived; the authors themselves flag this as potentially fragile. That tension needs to be resolved before the strong version of the claim can be accepted.

major comments (3)
  1. [Discussion and Supplementary Section III; Figs. 1(b), 4] The abstract states that the scaling analysis 'confirms' heating in the thermodynamic limit, but the evidence is strongest only for theta = pi/6 and pi/10. For small theta, e.g., theta = 0 in Fig. 1(b), the plateau height varies by roughly 5% over the accessible sizes L=8-18, and in Fig. 4(b) the fitted lambda for small theta exceeds the accessible L by an order of magnitude, so the fit covers far less than one e-fold. The analytic formula in Eq. (S6) gives lambda -> infinity as theta -> 0 and does not determine the perturbative lambda(0). In addition, Supplementary Section III explicitly states that the H2 spectrum splits into minibands whose merging at an inaccessible Lc may change the scaling abruptly, and the Discussion repeats this concern. These two points undermine the thermodynamic-limit conclusion precisely in the experimentally most relevant small-theta regime. I ask the authors to either provide additional evidence that the e^{-L/lambda} decay persists across the miniband merging (for example, larger-L overlap data, an effective-model argument, or a quantitative estimate of Lc) or to explicitly reword the abstract and conclusions to state that the no-DTC conclusion is provisional in this regime.
  2. [Results, Fig. 3; Conclusions] The paper asserts that the two pi-paired eigenstates 'determine the magnitude' of the subharmonic response (plateau height and Fourier peak), but no derivation or quantitative decomposition of Z(t) or |m~(0.5)| into contributions from these two states is provided for the perturbed model. The exponential suppression of the overlap in Fig. 4 is compared with the exponential suppression of the observables in Figs. 1-2, but the comparison is suggestive rather than rigorous. Since the central claim is that the response vanishes because the overlap vanishes, please provide a numerical check that the two-state contribution reproduces the plateau height (for example, by projecting the time evolution onto the two-state subspace and comparing Z(t) with the full result) or discuss in more detail why other eigenstates cannot contribute to the subharmonic response.
  3. [Results, first paragraph; Discussion] The statement that in the thermodynamic limit thermalization occurs over a timescale tau ~ 1/V, with V the magnitude of the integrability-breaking terms, is asserted to have been checked, but no supporting data or precise definition of V is shown. Because this point underlies the paper's distinction from prethermal DTCs and its claim that moderate-size clean systems can exhibit exponentially long subharmonic responses, please provide the numerical check or a precise operational definition of V.
minor comments (5)
  1. [Throughout] There are several typographical errors, including 'intergability' in the Results section, 'crstallinity' in the Results section, 'pleateau' in the Fig. 1 caption, and 'verfy' in Supplementary Section I; these should be corrected.
  2. [Fig. 4(b)] The axis label '100/lambda' is confusing: if the plotted quantity is 1/lambda, the label should be '1/lambda' or 'eta'; if 100/lambda is intended, the caption should explain the factor of 100.
  3. [Eq. (4)] The perturbation coefficients are described as 'drawn at random' and then given as fixed decimals; please state explicitly whether these values are a single fixed realization and whether any disorder average is performed for the homogeneous model (the Fig. 1 caption suggests time averaging only).
  4. [Figs. 1, 2, 4] The fitting procedure for the exponential decay (fit function, fitted L range, and statistical uncertainty) is not described; please add this information so the decay rate lambda(theta) is reproducible.
  5. [Supplementary Section I] In the sentence following Eq. (S5), 'the overlap of the initial condition with |down arrow,-->' appears to be a typo for '|up arrow,-- >'; the same calculation for |up arrow,--> is the one that yields the same result.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the exponential suppression is derived analytically in the integrable limit and checked against exact diagonalization, not imposed as an input.

full rationale

Every load-bearing step in the derivation is self-contained. The exponential suppression is not an input: the paper first observes the decay of the subharmonic plateau and spectral peak in exact diagonalization (Figs. 1–2), then identifies the two π-paired eigenstates (Fig. 3), and finally computes their overlap analytically in the integrable limit as [cos(θ/2)]^{2L}, giving λ(θ) = [−2 log(cos(θ/2))]^{-1} (Supplementary Section I, Eqs. S5–S7). The non-integrable λ is obtained by exponential fits to ED overlaps, and the same λ is used to characterize—not to define—the plateau decay. The thermodynamic-limit conclusion is an extrapolation of a numerically observed trend, which is a correctness risk (and is flagged by the authors themselves in Supplementary Section III), not a circular reduction. Self-citations to Refs. [8,9,10] occur only where standard DTC diagnostics are named, and the diagnostics are implemented independently via Eqs. (9)–(10); no load-bearing argument relies on those citations. No step reduces to its own input by construction.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central claim rests on the standard Floquet thermalization expectation, on the numerical persistence of two scar-like pi-paired eigenstates, and on the extrapolation of the observed exponential decay beyond numerically accessible sizes. These are stated or flagged by the authors. No new entities are introduced.

free parameters (2)
  • lambda(theta), system-size decay scale = up to ~650 near theta~0.1; e.g., lambda~400 from the integrable-limit formula at theta=0.1
    In Fig. 4 the authors fit the sum of the two largest overlaps to e^{-L/lambda}; lambda is the characteristic size at which the subharmonic response is suppressed. The functional form e^{-L/lambda} is predicted by the integrable-limit derivation, Eq. (S6), but for the non-integrable model lambda is extracted from the numerics.
  • small perturbation coefficients (Jz1, Jx1, hz1, Jx2, hz2, hx2) = given in text: ~0.0306, 0.0435, 0.0134, 0.0191, 0.0546, 0.0550
    Chosen by hand to be small and random so as to break integrability and hidden symmetries; they set the heating timescale tau ~ 1/V, but the central scaling claim is qualitatively independent of their precise values.
assumptions (3)
  • domain assumption Floquet systems of short-range interacting spins in the thermodynamic limit heat to an infinite-temperature-like featureless state (Floquet eigenstate thermalization hypothesis).
    The paper relies on this to conclude that the clean DTC response vanishes as L goes to infinity; it is invoked in the Introduction and Results, and is the standard expectation but not proven in the paper.
  • domain assumption The two special pi-paired eigenstates, approximately (|up> +/- |down>)/sqrt(2), remain the dominant contributors to the dynamics and retain their pi-pairing away from the integrable limit.
    This is established numerically (Fig. 3) for the accessible sizes but is assumed to hold for all L; it underlies the claim that the overlap with the initial condition sets the subharmonic response magnitude.
  • ad hoc to paper The exponential decay observed for L up to 18 continues to the thermodynamic limit and is not altered by the merging of H2 minibands at a larger critical size Lc.
    The authors explicitly flag this as a caveat in Supp. Sec. III: the miniband structure may change the scaling at L beyond exact diagonalization. The conclusion of no clean DTC depends on this continuation.

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Pith. "Pith review of To heat or not to heat: time crystallinity and finite-size effects in clean Floquet systems." pith.science (2026). https://pith.science/paper/VRJA6LTE

@misc{pith2026200913527,
  author       = {Pith},
  title        = {Pith review of: To heat or not to heat: time crystallinity and finite-size effects in clean Floquet systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VRJA6LTE}},
  note         = {Machine review of arXiv:2009.13527}
}
read the original abstract

A cornerstone assumption that most literature on discrete time crystals has relied on is that homogeneous Floquet systems generally heat to a featureless infinite temperature state, an expectation that motivated researchers in the field to mostly focus on many-body localized systems. Some works have however shown that the standard diagnostics for time crystallinity apply equally well to clean settings without disorder. This fact raises the question whether an homogeneous discrete time crystal is possible in which the originally expected heating is evaded. Studying both a localized and an homogeneous model with short-range interactions, we clarify this issue showing explicitly the key differences between the two cases. On the one hand, our careful scaling analysis confirms that, in the thermodynamic limit and in contrast to localized discrete time crystals, homogeneous systems indeed heat. On the other hand, we show that, thanks to a mechanism reminiscent of quantum scars, finite-size homogeneous systems can still exhibit very crisp signatures of time crystallinity. A subharmonic response can in fact persist over timescales that are much larger than those set by the integrability-breaking terms, with thermalization possibly occurring only at very large system sizes (e.g., of hundreds of spins). Beyond clarifying the emergence of heating in disorder-free systems, our work casts a spotlight on finite-size homogeneous systems as prime candidates for the experimental implementation of nontrivial out-of-equilibrium physics.

Figures

Figures reproduced from arXiv: 2009.13527 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
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Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

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Works this paper leans on

64 extracted references · 55 canonical work pages

  1. [1]

    Wilczek, Physical review letters 109, 160401 (2012)

    F. Wilczek, Physical review letters 109, 160401 (2012)

    work page 2012

  2. [2]

    Sacha, Physical Review A 91, 033617 (2015)

    K. Sacha, Physical Review A 91, 033617 (2015)

    2015

  3. [3]

    Khemani, A

    V . Khemani, A. Lazarides, R. Moessner, and S. L. Sondhi, Physical review letters 116, 250401 (2016)

    work page 2016

  4. [4]

    D. V . Else, B. Bauer, and C. Nayak, Physical review letters117, 090402 (2016)

    work page 2016

  5. [5]

    N. Y . Yao, A. C. Potter, I.-D. Potirniche, and A. Vishwanath, Physical review letters 118, 030401 (2017)

    work page 2017

  6. [6]

    F. M. Gambetta, F. Carollo, A. Lazarides, I. Lesanovsky, and J. P. Garrahan, Phys. Rev. E100, 060105 (2019)

    work page 2019

  7. [7]

    N. Y . Yao, C. Nayak, L. Balents, and M. P. Zaletel, Nature Physics , 1 (2020)

    work page 2020

  8. [8]

    Higher-order and fractional discrete time crystals in clean long-range interacting systems

    A. Pizzi, J. Knolle, and A. Nunnenkamp, arXiv preprint arXiv:1910.07539 (2019)

    work page Pith review arXiv 2019

Show all 64 references
  1. [9]

    Pizzi, J

    A. Pizzi, J. Knolle, and A. Nunnenkamp, Phys. Rev. Lett. 123, 150601 (2019)

    2019

  2. [10]

    Pizzi, A

    A. Pizzi, A. Nunnenkamp, and J. Knolle, arXiv preprint arXiv:2004.13034 (2020)

    2020 arXiv

  3. [11]

    Smits, L

    J. Smits, L. Liao, H. T. C. Stoof, and P. van der Straten, Phys. Rev. Lett. 121, 185301 (2018)

    2018

  4. [12]

    F. M. Surace, A. Russomanno, M. Dalmonte, A. Silva, R. Fazio, and F. Iemini, arXiv preprint arXiv:1811.12426 (2018)

    2018 arXiv

  5. [13]

    H. Zhao, F. Mintert, and J. Knolle, arXiv preprint arXiv:1906.06989 (2019)

    2019 arXiv

  6. [14]

    B. Zhu, J. Marino, N. Y . Yao, M. D. Lukin, and E. A. Demler, arXiv preprint arXiv:1904.01026 (2019)

    2019 arXiv

  7. [15]

    D. Malz, A. Pizzi, A. Nunnenkamp, and J. Knolle, arXiv preprint arXiv:2007.00979 (2020)

    2020 arXiv

  8. [16]

    Machado, D

    F. Machado, D. V . Else, G. D. Kahanamoku-Meyer, C. Nayak, and N. Y . Yao, Physical Review X10, 011043 (2020)

    2020

  9. [17]

    Z. Gong, R. Hamazaki, and M. Ueda, Physical review letters 120, 040404 (2018)

    2018

  10. [18]

    S. Choi, J. Choi, R. Landig, G. Kucsko, H. Zhou, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, V . Khemani, et al. , Nature 543, 221 (2017)

    2017

  11. [19]

    Zhang, P

    J. Zhang, P. Hess, A. Kyprianidis, P. Becker, A. Lee, J. Smith, G. Pagano, I.-D. Potirniche, A. C. Potter, A. Vishwanath,et al., Nature 543, 217 (2017)

    2017

  12. [20]

    Rovny, R

    J. Rovny, R. L. Blum, and S. E. Barrett, Physical review letters 120, 180603 (2018)

    2018

  13. [21]

    D. V . Else, B. Bauer, and C. Nayak, Phys. Rev. X 7, 011026 (2017)

    2017

  14. [22]

    D. V . Else, W. W. Ho, and P. T. Dumitrescu, Physical Review X 10, 021032 (2020)

    2020

  15. [23]

    Giergiel, A

    K. Giergiel, A. Kuro ´s, and K. Sacha, arXiv preprint arXiv:1807.02105 (2018)

    2018 arXiv

  16. [24]

    Matus and K

    P. Matus and K. Sacha, Phys. Rev. A 99, 033626 (2019)

    2019

  17. [25]

    Kshetrimayum, J

    A. Kshetrimayum, J. Eisert, and D. Kennes, arXiv preprint arXiv:2007.13820 (2020)

    2020 arXiv

  18. [26]

    H. E. Stanley, Rev. Mod. Phys. 71, S358 (1999)

    1999

  19. [27]

    C. W. von Keyserlingk, V . Khemani, and S. L. Sondhi, Physical Review B 94, 085112 (2016)

    2016

  20. [28]

    Lazarides, A

    A. Lazarides, A. Das, and R. Moessner, Physical Review E 90, 012110 (2014)

    2014

  21. [29]

    Ponte, A

    P. Ponte, A. Chandran, Z. Papi ´c, and D. A. Abanin, Annals of Physics 353, 196 (2015)

    2015

  22. [30]

    Ponte, Z

    P. Ponte, Z. Papi ´c, F. Huveneers, and D. A. Abanin, Physical review letters 114, 140401 (2015)

    2015

  23. [31]

    Lazarides, A

    A. Lazarides, A. Das, and R. Moessner, Physical review letters 115, 030402 (2015)

    2015

  24. [32]

    C. W. von Keyserlingk and S. L. Sondhi, Phys. Rev. B 93, 245146 (2016)

    2016

  25. [33]

    Moessner and S

    R. Moessner and S. L. Sondhi, Nature Physics 13, 424 (2017)

    2017

  26. [34]

    C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papi´c, Nature Physics 14, 745 (2018)

    2018

  27. [35]

    Prosen, Physical review letters 80, 1808 (1998)

    T. Prosen, Physical review letters 80, 1808 (1998)

    1998

  28. [36]

    Citro, E

    R. Citro, E. G. Dalla Torre, L. D’Alessio, A. Polkovnikov, M. Babadi, T. Oka, and E. Demler, Annals of Physics 360, 694 (2015)

    2015

  29. [37]

    Haldar, R

    A. Haldar, R. Moessner, and A. Das, Physical Review B 97, 245122 (2018). 8

    2018

  30. [38]

    Pai and M

    S. Pai and M. Pretko, Physical review letters 123, 136401 (2019)

    2019

  31. [39]

    Ji and B

    K. Ji and B. V . Fine, Physical Review Letters 107, 050401 (2011)

    2011

  32. [40]

    Ji and B

    K. Ji and B. V . Fine, Physical Review Letters 121, 050602 (2018)

    2018

  33. [41]

    M. Fava, R. Fazio, and A. Russomanno, Physical Review B 101, 064302 (2020)

    2020

  34. [42]

    Huang, Y .-H

    B. Huang, Y .-H. Wu, and W. V . Liu, Physical Review Letters 120, 110603 (2018)

    2018

  35. [43]

    W. C. Yu, J. Tangpanitanon, A. W. Glaetzle, D. Jaksch, and D. G. Angelakis, Physical Review A 99, 033618 (2019)

    2019

  36. [44]

    Yarloo, A

    H. Yarloo, A. E. Kopaei, and A. Langari, arXiv preprint arXiv:2007.14982 (2020)

    2020 arXiv

  37. [45]

    We show that under certain rather gen- eral and natural conditions thermalization only occurs at very large system sizes (of, e.g., many hundreds spins)

    holds rigorously only in the thermodynamic limit, and very large finite-size systems can possibly behave nontrivially for much longer times. We show that under certain rather gen- eral and natural conditions thermalization only occurs at very large system sizes (of, e.g., many ...

  38. [46]

    D. V . Else, C. Monroe, C. Nayak, and N. Y . Yao, Annual Re- view of Condensed Matter Physics 11, 467 (2020)

    2020

  39. [47]

    D. A. Abanin, W. De Roeck, W. W. Ho, and F. Huveneers, Physical Review B 95, 014112 (2017)

    2017

  40. [48]

    Abanin, W

    D. Abanin, W. De Roeck, W. W. Ho, and F. Huveneers, Com- munications in Mathematical Physics 354, 809 (2017)

    2017

  41. [49]

    D. J. Luitz, R. Moessner, S. Sondhi, and V . Khemani, Physical Review X 10, 021046 (2020)

    2020

  42. [50]

    F. M. Surace, M. V otto, E. G. Lazo, A. Silva, M. Dalmonte, and G. Giudici, arXiv preprint arXiv:2011.08218 (2020)

    2020 arXiv

  43. [51]

    Papi ´c, E

    Z. Papi ´c, E. M. Stoudenmire, and D. A. Abanin, Annals of Physics 362, 714 (2015)

    2015

  44. [52]

    S. Bera, G. De Tomasi, F. Weiner, and F. Evers, Physical Re- view Letters 118, 196801 (2017)

    2017

  45. [53]

    Weiner, F

    F. Weiner, F. Evers, and S. Bera, Physical Review B 100, 104204 (2019)

    2019

  46. [54]

    Abanin, J

    D. Abanin, J. Bardarson, G. De Tomasi, S. Gopalakrishnan, V . Khemani, S. Parameswaran, F. Pollmann, A. Potter, M. Ser- byn, and R. Vasseur, arXiv preprint arXiv:1911.04501 (2019)

    2019 arXiv

  47. [55]

    Sierant, D

    P. Sierant, D. Delande, and J. Zakrzewski, Physical Review Letters 124, 186601 (2020)

    2020

  48. [56]

    Altshuler, E

    B. Altshuler, E. Cuevas, L. Ioffe, and V . Kravtsov, Physical review letters 117, 156601 (2016)

    2016

  49. [57]

    Tikhonov, A

    K. Tikhonov, A. Mirlin, and M. Skvortsov, Physical Review B 94, 220203 (2016)

    2016

  50. [58]

    Abou-Chacra, D

    R. Abou-Chacra, D. Thouless, and P. Anderson, Journal of Physics C: Solid State Physics 6, 1734 (1973)

    1973

  51. [59]

    Parisi, S

    G. Parisi, S. Pascazio, F. Pietracaprina, V . Ros, and A. Scardic- chio, Journal of Physics A: Mathematical and Theoretical 53, 014003 (2019)

    2019

  52. [60]

    Kravtsov, B

    V . Kravtsov, B. Altshuler, and L. Ioffe, Annals of Physics 389, 148 (2018)

    2018

  53. [61]

    Tikhonov and A

    K. Tikhonov and A. Mirlin, Physical Review B 99, 214202 (2019)

    2019

  54. [62]

    Arute, K

    F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A. Buell, et al., Nature 574, 505 (2019)

    2019

  55. [63]

    Ippoliti, K

    M. Ippoliti, K. Kechedzhi, R. Moessner, S. Sondhi, and V . Khe- mani, arXiv preprint arXiv:2007.11602 (2020)

    2020 arXiv

  56. [64]

    To heat or not to heat: time crystallinity and finite-size effects in clean Floquet systems

    Y . Atas, E. Bogomolny, O. Giraud, and G. Roux, Physical re- view letters 110, 084101 (2013). Supplementary Information for “To heat or not to heat: time crystallinity and finite-size effects in clean Floquet systems” Andrea Pizzi, Daniel Malz, Giuseppe De Tomasi, Johannes Knol...

    2013

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