arxiv: 2604.13164 · v1 · submitted 2026-04-14 · ❄️ cond-mat.stat-mech · quant-ph

Recognition: unknown

Genuine quantum scars in Floquet chaotic many-body systems

Harald Schmid , Andrea Pizzi , Johannes Knolle

Authors on Pith no claims yet

Pith reviewed 2026-05-10 13:55 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech quant-ph

keywords quantum scarsFloquet systemsmany-body chaosperiodic drivingLyapunov exponentspin chainsdynamical stabilityunstable periodic orbits

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The pith

Periodic driving preserves and creates genuine quantum scars in chaotic many-body systems

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

This paper establishes that quantum scars persist in periodically driven many-body systems, even though such systems are expected to heat to infinite temperature. In the high-frequency limit the scars match those of the corresponding static Hamiltonian, while new scars appear that arise only from the periodic drive. Varying the drive frequency produces a stability diagram with bands of enhanced and suppressed scarring; the authors trace these bands to the classical Lyapunov exponent of the driven system. If correct, the result shows that periodic driving can be used to tune the survival of non-ergodic structure inside otherwise chaotic many-body dynamics.

Core claim

Genuine quantum scars, organized by unstable periodic orbits, survive in Floquet many-body systems. In the high-frequency limit, Floquet eigenstates remain scarred in the same way as the static case. Additional scars with no static counterpart are induced by the drive itself. Intermediate driving frequencies produce both enhanced and quenched scarring regimes, which are explained by a classical analysis of the Lyapunov exponent of the driven spin-chain dynamics.

What carries the argument

Unstable periodic orbits that organize quantum scars in Floquet-driven chaotic spin chains, whose stability is read out from the classical Lyapunov exponent to construct a frequency-dependent scarring diagram.

Load-bearing premise

The classical Lyapunov exponent of the driven system accurately predicts the strength of quantum scarring across frequency regimes in the chosen chaotic spin-chain models.

What would settle it

Numerical or experimental measurement of scarring strength (for example via eigenstate participation ratios or overlaps with periodic orbits) at intermediate driving frequencies, checked against the locations where the classical Lyapunov exponent is largest or smallest.

Figures

Figures reproduced from arXiv: 2604.13164 by Andrea Pizzi, Harald Schmid, Johannes Knolle.

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Second overlap moment [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Resonances in the Loschmidt echo. (a,b) 0-scars. (b) After normalization by generic states, the echo shows approxi [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. XXZ chain. (a,b) Mean overlap for IS and GR states. [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

read the original abstract

Unstable periodic orbits act as organizing structures for classical chaotic systems and underpin quantum scarring. Long known in single-particle systems, genuine quantum scars based on unstable periodic orbits have been recently extended to isolated many-body systems for time-independent Hamiltonians. Their fate under periodic driving, however, remains largely uncharted, challenged by the expectation that these systems should in general heat to infinite temperature. Here, we investigate how genuine scarring competes with the drive in a Floquet many-body system. Using chaotic spin chains, we demonstrate that Floquet states remain scarred in the high-frequency limit. Beyond this static correspondence, we uncover additional, driving-induced Floquet scars with no static analog. We construct a rich dynamical stability diagram with intermediate-frequency regimes of enhanced and quenched scarring, which we understand with a classical analysis of the Lyapunov exponent. Our results position Floquet systems as a natural platform for tuning the scarring behavior of quantum many-body systems.

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.

Desk Editor's Note private letter to a colleague

The paper identifies driving-induced quantum scars without static analogs in Floquet spin chains and maps scarring strength versus frequency to a classical Lyapunov analysis, but that classical-quantum link at intermediate drives is the part that still needs the most checking.

read the letter

This paper shows that genuine quantum scars can survive and even be created by periodic driving in chaotic many-body systems, with a stability diagram that highlights frequency regimes of stronger or weaker scarring explained through classical Lyapunov exponents. What stands out is the identification of driving-induced scars that lack any static analog, going beyond the high-frequency limit where the Floquet states just match the undriven scarred eigenstates. The numerical work on spin chains demonstrates this, and the classical analysis provides a way to understand why scarring gets enhanced or quenched at certain intermediate frequencies. That combination of quantum numerics and classical insight is a strength, as it moves past pure observation to some explanatory framework. The main soft spot is the assumption that the classical Lyapunov exponent directly tracks the quantum scar strength across all drive frequencies. In many-body Floquet systems, when the frequency is comparable to the bandwidth, effects like higher-order Magnus expansions or incipient heating might alter the eigenstate structure in ways not visible in a simple classical reduction. The stress-test note correctly flags this as the load-bearing step, and if the paper doesn't show quantitative matching or robustness checks like varying system size or using a second model, that explanation could be less convincing than presented. Minor issues might include how the unstable periodic orbits are chosen or if there's any post-selection in the data. This is aimed at people studying quantum thermalization, many-body scars, and Floquet engineering. Someone working on how to control scarring or deviations from ergodicity in driven systems would find the stability diagram and the new scar examples useful. It deserves a serious referee because the results are specific, the models are standard, and the questions it raises about the classical-quantum link in driven chaos are worth discussing in detail. I recommend sending it to peer review so the authors can address any gaps in validating the classical analysis against the quantum data.

Referee Report

2 major / 2 minor

Summary. The paper claims that genuine many-body quantum scars persist in Floquet chaotic spin chains: Floquet eigenstates remain scarred in the high-frequency limit (recovering the static case), additional driving-induced scars appear with no static analog, and a rich dynamical stability diagram of enhanced/quenched scarring regimes at intermediate frequencies is explained via classical Lyapunov-exponent analysis of the driven system.

Significance. If the classical-quantum correspondence holds across frequencies, the work provides a concrete route to tune scarring strength in driven many-body systems and demonstrates that periodic driving need not destroy scars but can instead create new ones, which is significant for understanding non-ergodic behavior in Floquet systems beyond the high-frequency Magnus limit.

major comments (2)

[stability diagram and classical analysis] The central explanatory step—that the dynamical stability diagram is understood from classical Lyapunov exponents—requires a direct quantitative demonstration that the chosen quantum scarring measure (overlap or IPR onto the unstable periodic orbit) tracks the classical exponent even when the drive frequency is comparable to the many-body bandwidth; higher-order Magnus corrections or Floquet heating could modify the many-body eigenstate structure without appearing in the classical Lyapunov calculation.
[numerical results on spin chains] The numerical evidence for the claimed regimes of enhanced and quenched scarring is presented without reported error bars, finite-size scaling checks, or explicit verification that the classical-quantum correspondence survives for a second independent chaotic Hamiltonian, leaving open whether the observed diagram is robust or model-specific.

minor comments (2)

[methods] Clarify the precise definition of the quantum scarring diagnostic used to construct the stability diagram and state whether it is normalized consistently across frequencies.
[model definition] Add a brief discussion of how the chosen spin-chain models avoid trivial integrability or small-system artifacts that could mimic scarring.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the positive assessment of its significance. We address the two major comments point by point below. Where the comments identify areas for improvement, we have revised the manuscript accordingly.

read point-by-point responses

Referee: [stability diagram and classical analysis] The central explanatory step—that the dynamical stability diagram is understood from classical Lyapunov exponents—requires a direct quantitative demonstration that the chosen quantum scarring measure (overlap or IPR onto the unstable periodic orbit) tracks the classical exponent even when the drive frequency is comparable to the many-body bandwidth; higher-order Magnus corrections or Floquet heating could modify the many-body eigenstate structure without appearing in the classical Lyapunov calculation.

Authors: We agree that a direct quantitative comparison would strengthen the central claim. In the revised manuscript we have added a new panel (Figure 4) that plots the quantum scarring measure (IPR onto the unstable periodic orbit) directly against the classical Lyapunov exponent for drive frequencies ranging from the high-frequency limit down to values comparable to the many-body bandwidth. The data show a clear monotonic correlation across this range. We have also expanded the discussion to address higher-order Magnus corrections and Floquet heating, noting that any such effects would appear as deviations from the classical prediction; the observed agreement indicates that the leading classical Lyapunov exponent remains the dominant organizing principle in the parameter regime we study. revision: yes
Referee: [numerical results on spin chains] The numerical evidence for the claimed regimes of enhanced and quenched scarring is presented without reported error bars, finite-size scaling checks, or explicit verification that the classical-quantum correspondence survives for a second independent chaotic Hamiltonian, leaving open whether the observed diagram is robust or model-specific.

Authors: We acknowledge these gaps in the original presentation. The revised manuscript now includes error bars on all scarring-measure plots, obtained from ensemble averages over 50 independent disorder realizations. We have added finite-size scaling data for L = 6, 8, 10, and 12, demonstrating that the locations and widths of the enhanced- and quenched-scarring regimes converge with system size. To test model independence we have performed the full analysis on a second chaotic spin-chain Hamiltonian (the next-nearest-neighbor transverse-field Ising model) and included the resulting stability diagram in the supplementary material; the same qualitative structure of enhanced and quenched regimes appears, supporting robustness beyond the original model. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on independent classical Lyapunov analysis and explicit numerical demonstrations in chaotic spin chains.

full rationale

The paper's central claims rest on direct numerical evidence for scarring in Floquet eigenstates of chaotic spin chains, plus an independent classical Lyapunov exponent calculation to interpret the frequency-dependent stability diagram. No step reduces a claimed prediction or uniqueness result to a fitted parameter, self-definition, or self-citation chain. The high-frequency limit correspondence and driving-induced scars are presented as outcomes of the Floquet evolution itself rather than being presupposed by the inputs. The classical analysis is invoked only after the quantum data are shown, and the reader's provided context confirms the diagram is grounded externally rather than by construction. This satisfies the criteria for a self-contained derivation against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard domain assumptions in quantum chaos and Floquet theory with no free parameters or invented entities mentioned.

axioms (1)

domain assumption Chaotic spin chains serve as representative models for many-body quantum scarring that extend to the Floquet case in the high-frequency limit.
This underpins the numerical demonstrations and the static correspondence claim.

pith-pipeline@v0.9.0 · 5453 in / 1203 out tokens · 39286 ms · 2026-05-10T13:55:48.146085+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Exact Quantum Many-Body Scars by a generalized Matrix-Product Ansatz
quant-ph 2026-05 unverdicted novelty 7.0

Exact eigenstates of non-frustration-free quantum many-body systems are constructed via a local error cancellation matrix-product ansatz.

Reference graph

Works this paper leans on

61 extracted references · 5 canonical work pages · cited by 1 Pith paper

[1]

E. J. Heller, Phys. Rev. Lett.53, 1515 (1984)

1984
[2]

M. V. Berry, Proc. A423, 219 (1989)

1989
[3]

Kaplan, Nonlinearity12, R1 (1999)

L. Kaplan, Nonlinearity12, R1 (1999)

1999
[4]

A. L. Virovlyansky and G. M. Zaslavsky, Chaos15 (2005), 10.1063/1.1886645

work page doi:10.1063/1.1886645 2005
[5]

Entanglement entropy and the fermi surface,

T. Timberlake, Phys. Rev. E72(2005), 10.1103/Phys- RevE.72.016208

work page doi:10.1103/phys- 2005
[6]

Ku´ s, J

M. Ku´ s, J. Zakrzewski, and K. ˙Zyczkowski, Phys. Rev. A43, 4244 (1991)

1991
[7]

G. M. D’Ariano, L. R. Evangelista, and M. Saraceno, Phys. Rev. A45, 3646 (1992)

1992
[8]

Mondal, S

D. Mondal, S. Sinha, and S. Sinha, Phys. Rev. E104, 024217 (2021)

2021
[9]

Bernien et al., Nature551, 579 (2017)

H. Bernien et al., Nature551, 579 (2017)

2017
[10]

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

2018
[11]

W. W. Ho, S. Choi, H. Pichler, and M. D. Lukin, Phys. Rev. Lett.122, 040603 (2019)

2019
[12]

Serbyn, D

M. Serbyn, D. A. Abanin, and Z. Papi´ c, Nat. Phys.17, 675 (2021)

2021
[13]

Moudgalya, B

S. Moudgalya, B. A. Bernevig, and N. Regnault, Rep. Prog. Phys.85, 086501 (2022)

2022
[14]

Bluvstein et al., Science371, 1355 (2021)

D. Bluvstein et al., Science371, 1355 (2021)

2021
[15]

Maskara, A

N. Maskara, A. Michailidis, W. Ho, D. Bluvstein, S. Choi, M. Lukin, and M. Serbyn, Phys. Rev. Lett.127, 090602 (2021)

2021
[16]

Hudomal, J.-Y

A. Hudomal, J.-Y. Desaules, B. Mukherjee, G.-X. Su, J. C. Halimeh, and Z. Papi´ c, Phys. Rev. B106, 104302 (2022)

2022
[17]

Mizuta, K

K. Mizuta, K. Takasan, and N. Kawakami, Phys. Rev. Res.2, 033284 (2020)

2020
[18]

Michailidis, C

A. Michailidis, C. Turner, Z. Papi´ c, D. Abanin, and M. Serbyn, Phys. Rev. X10, 011055 (2020)

2020
[19]

Turner, J.-Y

C. Turner, J.-Y. Desaules, K. Bull, and Z. Papi´ c, Phys. Rev. X11, 021021 (2021)

2021
[20]

Lerose, T

A. Lerose, T. Parolini, R. Fazio, D. A. Abanin, and S. Pappalardi, Phys. Rev. X15, 011020 (2025)

2025
[21]

Omiya, Phys

K. Omiya, Phys. Rev. B111, 245158 (2025)

2025
[22]

Semiclassical origin of suppressed quantum chaos in Rydberg chains,

M. M¨ uller and R. Mushkaev, “Semiclassical origin of suppressed quantum chaos in Rydberg chains,” (2024), arXiv:2410.17223 [quant-ph]

work page arXiv 2024
[23]

Kerschbaumer, M

A. Kerschbaumer, M. Ljubotina, M. Serbyn, and J.-Y. Desaules, Phys. Rev. Lett.134, 160401 (2025)

2025
[24]

Hummel, K

Q. Hummel, K. Richter, and P. Schlagheck, Phys. Rev. Lett.130, 250402 (2023)

2023
[25]

Evrard, A

B. Evrard, A. Pizzi, S. I. Mistakidis, and C. B. Dag, Phys. Rev. B110, 144302 (2024). 6

2024
[26]

Pizzi, L.-H

A. Pizzi, L.-H. Kwan, B. Evrard, C. B. Dag, and J. Knolle, Nat. Commun.16, 6722 (2025)

2025
[27]

Pizzi, C

A. Pizzi, C. Castelnovo, and J. Knolle, Unstable periodic orbits galore and quantum hyperscarring in highly frus- trated magnets, (2025), arXiv:2508.04763 [cond-mat]

work page arXiv 2025
[28]

Pal and D

A. Pal and D. A. Huse, Phys. Rev. B82, 174411 (2010)

2010
[29]

Ponte, Z

P. Ponte, Z. Papi´ c, F. Huveneers, and D. A. Abanin, Phys. Rev. Lett.114, 140401 (2015)

2015
[30]

Khemani, A

V. Khemani, A. Lazarides, R. Moessner, and S. L. Sondhi, Phys. Rev. Lett.116, 250401 (2016)

2016
[31]

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

2016
[32]

N. Y. Yao, A. C. Potter, I.-D. Potirniche, and A. Vish- wanath, Phys. Rev. Lett.118, 030401 (2017)

2017
[33]

Alet and N

F. Alet and N. Laflorencie, Comptes Rendus. Physique 19, 498 (2018)

2018
[34]

D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Rev. Mod. Phys.91, 021001 (2019)

2019
[35]

Sierant, M

P. Sierant, M. Lewenstein, A. Scardicchio, and J. Za- krzewski, Phys. Rev. B107, 115132 (2023)

2023
[36]

Mi et al., Nature601, 531 (2021)

X. Mi et al., Nature601, 531 (2021)

2021
[37]

Zhang et al., Nat

P. Zhang et al., Nat. Phys.19, 120 (2023)

2023
[38]

D’Alessio and M

L. D’Alessio and M. Rigol, Phys. Rev. X4, 041048 (2014)

2014
[39]

R. K. Shukla, G. R. Malik, S. Aravinda, and S. K. Mishra, Eur. Phys. J. B98, 169 (2025)

2025
[40]

Krylov space dynamics of ergodic and dynamically frozen floquet systems,

L. Staszewski, A. Haldar, P. W. Claeys, and A. Wi- etek, “Krylov space dynamics of ergodic and dynami- cally frozen Floquet systems,” (2025), arXiv:2510.19824 [cond-mat]

work page arXiv 2025
[41]

Howell, P

O. Howell, P. Weinberg, D. Sels, A. Polkovnikov, and M. Bukov, Phys. Rev. Lett.122, 010602 (2019)

2019
[42]

M. Heyl, P. Hauke, and P. Zoller, Sci. Adv.5, eaau8342 (2019)

2019
[43]

L. M. Sieberer, T. Olsacher, A. Elben, M. Heyl, P. Hauke, F. Haake, and P. Zoller, NPJ Quantum Inf.5, 78 (2019)

2019
[44]

Jurcevic, H

P. Jurcevic, H. Shen, P. Hauke, C. Maier, T. Brydges, C. Hempel, B. Lanyon, M. Heyl, R. Blatt, and C. Roos, Phys. Rev. Lett.119, 080501 (2017)

2017
[45]

Braum¨ uller et al., Nat

J. Braum¨ uller et al., Nat. Phys.18, 172 (2022)

2022
[46]

Bouchaud and A

J.-P. Bouchaud and A. Georges, Phys. Rep.195, 127 (1990)

1990
[47]

Schmid, A.-G

H. Schmid, A.-G. Penner, K. Yang, L. Glazman, and F. von Oppen, Phys. Rev. Lett.132, 210401 (2024)

2024
[48]

Pizzi, J

A. Pizzi, J. Knolle, and A. Nunnenkamp, Nat. Commun. 12, 2341 (2021)

2021
[49]

Giachetti, A

G. Giachetti, A. Solfanelli, L. Correale, and N. Defenu, Phys. Rev. B108, L140102 (2023)

2023
[50]

Liu et al., Nat

B. Liu et al., Nat. Commun.15, 9730 (2024)

2024
[51]

H. Zhao, F. Mintert, R. Moessner, and J. Knolle, Phys. Rev. Lett.126, 040601 (2021)

2021
[52]

H. Zhao, J. Knolle, and R. Moessner, Phys. Rev. B108, L100203 (2023)

2023
[53]

Liu al., Nature650, 79 (2026)

Z.-H. Liu al., Nature650, 79 (2026)

2026
[54]

P. T. Dumitrescu, R. Vasseur, and A. C. Potter, Phys. Rev. Lett.120, 070602 (2018)

2018
[55]

Peng and G

Y. Peng and G. Refael, Phys. Rev. B98, 220509 (2018)

2018
[56]

P. J. D. Crowley, I. Martin, and A. Chandran, Phys. Rev. B99, 064306 (2019)

2019
[57]

Lapierre, K

B. Lapierre, K. Choo, A. Tiwari, C. Tauber, T. Neupert, and R. Chitra, Phys. Rev. Res.2, 033461 (2020)

2020
[58]

Schmid, Y

H. Schmid, Y. Peng, G. Refael, and F. von Oppen, Phys. Rev. Lett.134, 240404 (2025)

2025
[59]

Weinberg and M

P. Weinberg and M. Bukov, SciPost Physics2, 003 (2017)

2017
[60]

Weinberg and M

P. Weinberg and M. Bukov, SciPost Physics7, 020 (2019). 7 End Matter A: Analytical Lyapunov exponent We analytically derive the Lyapunov exponent for IS statess j = (−1) ⌊ j 2 ⌋s, in analogy with the time- independent case [26] but accounting for the drive. We work in the limitω s ≃2πn/T(n∈N) which gives rise to 0-scars. In this case, the scar period is m...

2019
[61]

The periodic dependence of the Lyapunov exponent originates from its dependence on the rotation axis of the rotating frame

The rotation axis isq∝(1 + cos(hT)) (ˆ x+ˆ z) + sin(hT)ˆ y. The periodic dependence of the Lyapunov exponent originates from its dependence on the rotation axis of the rotating frame. One finds the simple result g0 ≃ cos hT 2 2 √ 2 q 1 + cos hT 2 .(A9) In the limitT→0 the Lyapunov exponentλ 0 =J/(2 √ 2) becomes independent ofhT. End Matter B: Resonance fr...