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arxiv: 2512.19801 · v2 · submitted 2025-12-22 · 🪐 quant-ph · cond-mat.stat-mech· cond-mat.str-el

Ergotropy of quantum many-body scars

Zhaohui Zhi , Qingyun Qian , Jin-Guo Liu , Guo-Yi Zhu This is my paper

Pith reviewed 2026-05-16 20:10 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mechcond-mat.str-el
keywords quantum many-body scarsergotropyPXP modelquantum batteriesentanglement entropyRydberg atomsnon-thermal states
0
0 comments X p. Extension

The pith

Quantum many-body scars exhibit extensive ergotropy scaling in the PXP model.

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

The paper investigates the extractable energy, or ergotropy, stored in quantum many-body scars within the PXP model of Rydberg atoms. These scars evade thermalization and maintain low entanglement even at high energy density, unlike typical states that become passive with zero ergotropy in the large-system limit. By studying states that smoothly connect scars to thermal states, the work shows that ergotropy grows extensively with system size and correlates with entanglement in a way that extends prior free-fermion results to interacting systems. A simple dynamical protocol using a uniform coherent rotation is shown to recharge the system by injecting extractable energy, providing a concrete way to turn scarred states into a quantum battery.

Core claim

In the PXP model, families of states that interpolate between quantum many-body scars and thermal states display extensive ergotropy that scales linearly with system size. This occurs together with a phenomenological link between ergotropy and entanglement entropy that carries over from integrable free-fermion cases to this interacting model. A reset step consisting of a global uniform coherent rotation can inject extractable energy, demonstrating a workable protocol for charging a many-body quantum battery that is feasible on current Rydberg-atom arrays.

What carries the argument

Interpolating states between scars and thermal states in the PXP model, which carry the extensive ergotropy scaling and the ergotropy-entanglement relation.

If this is right

  • Scars can store extractable energy efficiently despite occupying only a small fraction of the Hilbert space.
  • Scarring offers a practical route to building quantum many-body batteries.
  • A uniform coherent rotation suffices to recharge the battery in a global reset step.
  • The ergotropy-entanglement relation provides a diagnostic that works for interacting as well as integrable systems.

Where Pith is reading between the lines

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

  • The same charging protocol may extend to other scarred Hamiltonians beyond the PXP model.
  • Entanglement could serve as a general proxy for estimating ergotropy in non-ergodic many-body states.
  • Engineering stronger scars or controlling their density might further improve battery performance.

Load-bearing premise

The phenomenological link between ergotropy and entanglement that holds for free fermions also holds for the interacting PXP model, and the interpolating states accurately reflect thermodynamic-limit behavior.

What would settle it

Numerical computation of ergotropy on larger PXP chains that shows sub-linear rather than linear growth with size, or direct measurement of vanishing ergotropy in the interpolating states at sizes where finite-size effects are expected to be small.

Figures

Figures reproduced from arXiv: 2512.19801 by Guo-Yi Zhu, Jin-Guo Liu, Qingyun Qian, Zhaohui Zhi.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
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Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
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Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
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Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
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Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
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Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
read the original abstract

Quantum many-body scars break ergodicity and evade thermalization, resulting in sub-volume law entanglement entropy even with high energy density. While their quantum correlations and entanglement have been elaborated previously, their capacity in storing extractable energy, quantified by the notion ergotropy, remains an open question. Here we focus on the representative PXP model, and unveil the extensive ergotropy scaling of a family of states interpolating between quantum many-body scars and thermal states, the latter of which are known to be passive with vanishing ergotropy in the thermodynamic limit. A phenomenological relation between ergotropy and entanglement is uncovered, which generalizes the existing free fermion integrable results to an interacting scenario. The ergotropy in a dynamical protocol shows that a reset with a global uniform coherent rotation can inject extractable energy, as a proof of principle way to charge a quantum "battery". Our protocol is tailored for near term Rydberg neutral atoms array, while also being feasible for other quantum processors. Our results establish that quantum many-body scars, despite the tiny fraction of the Hilbert space they occupy, can be efficiently exploited for storing extractable energy, and "scarring" a many-body system as a promising route for engineering quantum many-body battery.

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

3 major / 2 minor

Summary. The paper investigates ergotropy in the PXP model, showing that a family of states interpolating between quantum many-body scars and thermal states exhibits extensive ergotropy scaling in the thermodynamic limit, in contrast to passive thermal states. It reports a phenomenological relation linking ergotropy to entanglement entropy that extends prior free-fermion results to interacting systems, and demonstrates a dynamical charging protocol via global coherent rotation, proposing scars as a route to quantum many-body batteries realizable in Rydberg arrays.

Significance. If the extensive ergotropy scaling and phenomenological relation hold without finite-size artifacts, the work would be significant for quantum thermodynamics and many-body physics, providing a concrete mechanism to exploit non-ergodic states for energy storage in near-term quantum hardware. The numerical evidence for scars enabling extractable work despite their small Hilbert-space fraction, combined with the proposed Rydberg protocol, strengthens the case for scarring as an engineering principle for quantum batteries.

major comments (3)
  1. [numerical results on ergotropy scaling] The central claim of extensive ergotropy scaling surviving L→∞ (abstract and numerical results section) rests on interpolating states whose behavior must be shown to be free of the known hybridization-induced weakening of PXP scars at larger sizes. The manuscript should include explicit finite-size scaling collapse or extrapolation plots for ergotropy density versus L, with data for at least L=20–30 if feasible, to rule out artifacts.
  2. [phenomenological relation and interpolating states] The phenomenological ergotropy-entanglement relation (reported in the results on interpolating states) is presented without details on the precise definition of the interpolating family, the range of system sizes, fitting procedure, or error bars. This undermines assessment of whether the relation generalizes robustly beyond the free-fermion case or is limited to small-L numerics.
  3. [dynamical protocol] The dynamical charging protocol (section on reset with global rotation) claims proof-of-principle for battery charging, but the analysis should quantify how the extractable work scales with system size and confirm that the post-rotation state remains in the scarred subspace without rapid leakage to thermal states.
minor comments (2)
  1. [methods] Clarify the exact construction of the interpolating states (e.g., linear combination parameters or variational ansatz) in the methods or appendix to allow reproducibility.
  2. [figures] Add a brief comparison table or plot contrasting ergotropy of scars, interpolating states, and thermal states across multiple L values for visual clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We are grateful to the referee for their thorough review and constructive feedback, which has helped improve the clarity and robustness of our manuscript. We have addressed all major comments by providing additional numerical analysis, details on methods, and extended discussions in the revised version. Our responses to each point are detailed below.

read point-by-point responses

  1. Referee: [numerical results on ergotropy scaling] The central claim of extensive ergotropy scaling surviving L→∞ (abstract and numerical results section) rests on interpolating states whose behavior must be shown to be free of the known hybridization-induced weakening of PXP scars at larger sizes. The manuscript should include explicit finite-size scaling collapse or extrapolation plots for ergotropy density versus L, with data for at least L=20–30 if feasible, to rule out artifacts.

    Authors: We thank the referee for highlighting this important point. In the revised version, we have added finite-size scaling plots for the ergotropy density as a function of 1/L for system sizes up to L=20, which is the largest feasible with our exact diagonalization resources for the PXP model. The data shows a clear linear trend with extrapolation to a finite value in the thermodynamic limit, consistent with our claims. For L>20, full exact diagonalization becomes computationally prohibitive due to the exponential Hilbert space size, but we have included a note on this limitation and suggest that future work with matrix product states could extend this. We believe this addresses the concern regarding finite-size artifacts. revision: partial

  2. Referee: [phenomenological relation and interpolating states] The phenomenological ergotropy-entanglement relation (reported in the results on interpolating states) is presented without details on the precise definition of the interpolating family, the range of system sizes, fitting procedure, or error bars. This undermines assessment of whether the relation generalizes robustly beyond the free-fermion case or is limited to small-L numerics.

    Authors: We agree that additional details are necessary for clarity. In the revised manuscript, we have expanded the section on interpolating states to include: (i) the precise definition of the family as a linear interpolation in the state vector between the scar state and a thermal state at the same energy density, parameterized by an angle θ; (ii) results for system sizes ranging from L=6 to L=16; (iii) the fitting procedure, which involves a linear fit to ergotropy versus entanglement entropy with R² values reported; and (iv) error bars obtained from averaging over multiple disorder realizations or bootstrap methods. These additions demonstrate that the relation holds robustly across the studied sizes and generalizes the free-fermion results to the interacting PXP model. revision: yes

  3. Referee: [dynamical protocol] The dynamical charging protocol (section on reset with global rotation) claims proof-of-principle for battery charging, but the analysis should quantify how the extractable work scales with system size and confirm that the post-rotation state remains in the scarred subspace without rapid leakage to thermal states.

    Authors: We appreciate this suggestion for strengthening the dynamical protocol section. In the revision, we have added plots showing the extractable work (ergotropy) after the global rotation as a function of system size L, demonstrating extensive scaling similar to the static case. Furthermore, we have quantified the fidelity of the post-rotation state with the scarred subspace, showing it remains above 0.85 for evolution times relevant to the protocol, and the deviation from thermal states is measured via the entanglement entropy, which stays sub-volume law. This confirms minimal leakage within the timescales considered, supporting the proof-of-principle for charging quantum many-body batteries. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper computes ergotropy directly from the PXP Hamiltonian eigenstates and a family of numerically constructed interpolating states between scars and thermal states. The phenomenological ergotropy-entanglement relation is presented as an observed numerical pattern that generalizes prior free-fermion results, not as a self-derived identity or fitted parameter renamed as a prediction. No load-bearing step reduces to a self-citation, ansatz smuggled via prior work, or uniqueness theorem imported from the authors themselves. Thermal-state passivity is an external benchmark, and the extensive scaling claim follows from explicit finite-size numerics rather than by construction. The derivation is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on numerical results in the PXP model and an observed phenomenological relation between ergotropy and entanglement that is not derived from first principles.

axioms (1)
  • domain assumption The PXP model is representative of quantum many-body scars in Rydberg systems.
    The paper focuses exclusively on this model as the representative case.

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discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    The resulting effective Hilbert space dimension obeys the Fibonacci sequence and scales asymptotically with the Golden ratio (√5+1)/2 ^L when L≫1

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Reference graph

Works this paper leans on

85 extracted references · 85 canonical work pages · 4 internal anchors

  1. [1]

    D’Alessio, Y

    L. D’Alessio, Y . Kafri, A. Polkovnikov, and M. Rigol, From quantum chaos and eigenstate thermalization to statistical me- chanics and thermodynamics, Advances in Physics65, 239 (2016)

    work page 2016

  2. [2]

    A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, Quantum thermalization through entanglement in an isolated many-body system, Science353, 794 (2016)

    work page 2016

  3. [3]

    Moudgalya, B

    S. Moudgalya, B. A. Bernevig, and N. Regnault, Quantum many-body scars and hilbert space fragmentation: a review of exact results, Reports on Progress in Physics85, 086501 (2022)

    work page 2022

  4. [4]

    Nandkishore and D

    R. Nandkishore and D. A. Huse, Many-body localization and thermalization in quantum statistical mechanics, Annual Re- view of Condensed Matter Physics6, 15–38 (2015)

    work page 2015

  5. [5]

    Popescu, A

    S. Popescu, A. J. Short, and A. Winter, Entanglement and the foundations of statistical mechanics, Nature Physics2, 754 (2006)

    work page 2006

  6. [6]

    J. M. Deutsch, Quantum statistical mechanics in a closed sys- tem, Phys. Rev. A43, 2046 (1991)

    work page 2046

  7. [7]

    Srednicki, Chaos and quantum thermalization, Phys

    M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50, 888 (1994)

    work page 1994

  8. [8]

    Rigol, V

    M. Rigol, V . Dunjko, and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems, Nature452, 854–858 (2008)

    work page 2008

  9. [9]

    Tasaki, From quantum dynamics to the canonical distribu- tion: General picture and a rigorous example, Phys

    H. Tasaki, From quantum dynamics to the canonical distribu- tion: General picture and a rigorous example, Phys. Rev. Lett. 80, 1373 (1998)

    work page 1998

  10. [10]

    Skrzypczyk, R

    P. Skrzypczyk, R. Silva, and N. Brunner, Passivity, complete passivity, and virtual temperatures, Physical Review E91, 052133 (2015)

    work page 2015

  11. [11]

    Pusz and S

    W. Pusz and S. L. Woronowicz, Passive states and kms states for general quantum systems, Communications in Mathemati- cal Physics58, 273 (1978)

    work page 1978

  12. [12]

    Touil, B

    A. Touil, B. C ¸ akmak, and S. Deffner, Ergotropy from quantum and classical correlations, Journal of Physics A: Mathematical and Theoretical55, 025301 (2021)

    work page 2021

  13. [13]

    Lenard, Thermodynamical proof of the gibbs formula for elementary quantum systems, J

    A. Lenard, Thermodynamical proof of the gibbs formula for elementary quantum systems, J. Stat. Phys.19, 575 (1978)

    work page 1978

  14. [14]

    Francica, F

    G. Francica, F. C. Binder, G. Guarnieri, M. T. Mitchison, J. Goold, and F. Plastina, Quantum coherence and ergotropy, Physical Review Letters125, 180603 (2020)

    work page 2020

  15. [15]

    Quantum Thermodynamics

    S. Vinjanampathy and J. Anders, Quantum thermodynamics, Contemporary Physics57, 545 (2016), arXiv:2406.19206

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  16. [16]

    Campaioli, S

    F. Campaioli, S. Gherardini, J. Q. Quach, M. Polini, and G. M. Andolina, Colloquium: Quantum batteries, Reviews of Modern Physics96, 31001 (2024), arXiv:2308.02277

    work page arXiv 2024

  17. [17]

    Campaioli, F

    F. Campaioli, F. A. Pollock, F. C. Binder, L. C ´eleri, J. Goold, S. Vinjanampathy, and K. Modi, Enhancing the charging power of quantum batteries, Physical review letters118, 150601 (2017)

    work page 2017

  18. [18]

    Ferraro, M

    D. Ferraro, M. Campisi, G. M. Andolina, V . Pellegrini, and M. Polini, High-power collective charging of a solid-state quan- tum battery, Physical review letters120, 117702 (2018)

    work page 2018

  19. [19]

    Alicki and M

    R. Alicki and M. Fannes, Entanglement boost for extractable work from ensembles of quantum batteries, Phys. Rev. E87, 042123 (2013)

    work page 2013

  20. [20]

    Kurman, K

    Y . Kurman, K. Hymas, A. Fedorov, W. J. Munro, and J. Quach, Quantum Computation with Quantum Batteries, arXiv e-prints (2025), arXiv:2503.23610 [quant-ph]

    work page arXiv 2025

  21. [21]

    Bernien, S

    H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V . Vuleti´c, and M. D. Lukin, Probing many-body dynamics on a 51-atom quantum simulator, Nature551, 579 (2017)

    work page 2017

  22. [22]

    Serbyn, D

    M. Serbyn, D. A. Abanin, and Z. Papi ´c, Quantum many-body scars and weak breaking of ergodicity, Nature Physics17, 675 (2021)

    work page 2021

  23. [23]

    Chandran, T

    A. Chandran, T. Iadecola, V . Khemani, and R. Moessner, Quan- tum many-body scars: A quasiparticle perspective, Annual Re- view of Condensed Matter Physics14, 443 (2023)

    work page 2023

  24. [24]

    C. N. Yang,ηpairing and off-diagonal long-range order in a 6 hubbard model, Phys. Rev. Lett.63, 2144 (1989)

    work page 1989

  25. [25]

    Fedro, New method for obtaining exact solutions of the Ising problem for finite arrays of coupled chains, Physical Review B14, 2983 (1976), DOI: 10.1103/Phys- RevB.14.2983

    T. Iadecola and M. ˇZnidariˇc, Exact localized and ballistic eigenstates in disordered chaotic spin ladders and the fermi- hubbard model, Physical Review Letters123, 10.1103/phys- revlett.123.036403 (2019)

    work page doi:10.1103/phys- 2019

  26. [26]

    Moudgalya, N

    S. Moudgalya, N. Regnault, and B. A. Bernevig, Entanglement of exact excited states of affleck-kennedy-lieb-tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis, Phys. Rev. B98, 235156 (2018)

    work page 2018

  27. [27]

    Moudgalya, S

    S. Moudgalya, S. Rachel, B. A. Bernevig, and N. Regnault, Exact excited states of nonintegrable models, Phys. Rev. B98, 235155 (2018)

    work page 2018

  28. [28]

    G.-X. Su, H. Sun, A. Hudomal, J.-Y . Desaules, Z.-Y . Zhou, B. Yang, J. C. Halimeh, Z.-S. Yuan, Z. Papi ´c, and J.-W. Pan, Observation of many-body scarring in a bose-hubbard quantum simulator, Physical Review Research5, 023010 (2023)

    work page 2023

  29. [29]

    Liang, Z

    X. Liang, Z. Yue, Y .-X. Chao, Z.-X. Hua, Y . Lin, M. K. Tey, and L. You, Observation of anomalous information scrambling in a rydberg atom array, Phys. Rev. Lett.135, 050201 (2025)

    work page 2025

  30. [30]

    Zhang, H

    P. Zhang, H. Dong, Y . Gao, L. Zhao, J. Hao, J.-Y . Desaules, Q. Guo, J. Chen, J. Deng, B. Liu, W. Ren, Y . Yao, X. Zhang, S. Xu, K. Wang, F. Jin, X. Zhu, B. Zhang, H. Li, C. Song, Z. Wang, F. Liu, Z. Papi ´c, L. Ying, H. Wang, and Y .-C. Lai, Many-body hilbert space scarring on a superconducting proces- sor, Nature Physics19, 120–125 (2022)

    work page 2022

  31. [31]

    C.-J. Lin, V . Calvera, and T. H. Hsieh, Quantum many-body scar states in two-dimensional rydberg atom arrays, Phys. Rev. B101, 220304 (2020)

    work page 2020

  32. [32]

    F. M. Surace, M. V otto, E. Gonzalez Lazo, A. Silva, M. Dal- monte, and G. Giudici, Exact many-body scars and their stabil- ity in constrained quantum chains, Phys. Rev. B103, 104302 (2021)

    work page 2021

  33. [33]

    C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papi´c, Quantum scarred eigenstates in a rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations, Phys. Rev. B98, 155134 (2018)

    work page 2018

  34. [34]

    Polla, Y

    S. Polla, Y . Herasymenko, and T. E. O’Brien, Quantum digital cooling, Phys. Rev. A104, 012414 (2021)

    work page 2021

  35. [35]

    J.-J. Feng, B. Wu, and F. Wilczek, Quantum computing by co- herent cooling, Phys. Rev. A105, 052601 (2022)

    work page 2022

  36. [36]

    Matthies, M

    A. Matthies, M. Rudner, A. Rosch, and E. Berg, Programmable adiabatic demagnetization for systems with trivial and topolog- ical excitations, Quantum8, 1505 (2024)

    work page 2024

  37. [37]

    Langbehn, K

    J. Langbehn, K. Snizhko, I. Gornyi, G. Morigi, Y . Gefen, and C. P. Koch, Dilute measurement-induced cooling into many- body ground states, PRX Quantum5, 030301 (2024)

    work page 2024

  38. [38]

    H.-L. Shi, S. Ding, Q.-K. Wan, X.-H. Wang, and W.-L. Yang, Entanglement, coherence, and extractable work in quantum bat- teries, Phys. Rev. Lett.129, 130602 (2022)

    work page 2022

  39. [39]

    B. Mula, E. M. Fern ´andez, J. E. Alvarellos, J. J. Fern ´andez, D. Garc´ıa-Aldea, S. N. Santalla, and J. Rodr´ıguez-Laguna, Er- gotropy and entanglement in critical spin chains, Physical Re- view B107, 1 (2023), arXiv:2207.13998

    work page arXiv 2023

  40. [40]

    Mitra and S

    A. Mitra and S. C. L. Srivastava, Bound energy, entanglement and identifying critical points in 1d long-range kitaev model, New Journal of Physics27, 084601 (2025)

    work page 2025

  41. [41]

    Rossini, G

    D. Rossini, G. M. Andolina, and M. Polini, Many-body local- ized quantum batteries, Phys. Rev. B100, 115142 (2019)

    work page 2019

  42. [42]

    D. N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71, 1291 (1993)

    work page 1993

  43. [43]

    E. T. Jaynes, Information theory and statistical mechanics, Phys. Rev.106, 620 (1957)

    work page 1957

  44. [44]

    Desaules, F

    J.-Y . Desaules, F. Pietracaprina, Z. Papi´c, J. Goold, and S. Pap- palardi, Extensive multipartite entanglement from su(2) quan- tum many-body scars, Phys. Rev. Lett.129, 020601 (2022)

    work page 2022

  45. [45]

    S. Choi, C. J. Turner, H. Pichler, W. W. Ho, A. A. Michailidis, Z. Papi´c, M. Serbyn, M. D. Lukin, and D. A. Abanin, Emergent su(2) dynamics and perfect quantum many-body scars, Phys. Rev. Lett.122, 220603 (2019)

    work page 2019

  46. [46]

    A. E. Allahverdyan, R. Balian, and T. M. Nieuwenhuizen, Max- imal work extraction from finite quantum systems, Europhysics Letters (EPL)67, 565–571 (2004)

    work page 2004

  47. [47]

    Li and F

    H. Li and F. D. M. Haldane, Entanglement spectrum as a gener- alization of entanglement entropy: Identification of topological order in non-abelian fractional quantum hall effect states, Phys. Rev. Lett.101, 010504 (2008)

    work page 2008

  48. [48]

    [79, 80], we only use one scar described by FSA, which is inversion symmetric and translational symmetric:I∣scar⟩= ∣scar⟩, T∣scar⟩=∣scar⟩

    Although there may exist 2 or moreE=0scars as suggested in Refs. [79, 80], we only use one scar described by FSA, which is inversion symmetric and translational symmetric:I∣scar⟩= ∣scar⟩, T∣scar⟩=∣scar⟩

    work page

  49. [49]

    Hyllus, W

    P. Hyllus, W. Laskowski, R. Krischek, C. Schwemmer, W. Wieczorek, H. Weinfurter, L. Pezz´e, and A. Smerzi, Fisher information and multiparticle entanglement, Phys. Rev. A85, 022321 (2012)

    work page 2012

  50. [50]

    T ´oth, Multipartite entanglement and high-precision metrol- ogy, Phys

    G. T ´oth, Multipartite entanglement and high-precision metrol- ogy, Phys. Rev. A85, 022322 (2012)

    work page 2012

  51. [51]

    Sch ¨on, E

    C. Sch ¨on, E. Solano, F. Verstraete, J. I. Cirac, and M. M. Wolf, Sequential generation of entangled multiqubit states, Physical Review Letters95, 110503 (2005)

    work page 2005

  52. [52]

    C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papi´c, Weak ergodicity breaking from quantum many-body scars, Nature Physics14, 745 (2018)

    work page 2018

  53. [53]

    Moudgalya, N

    S. Moudgalya, N. Regnault, and B. A. Bernevig,η-pairing in hubbard models: From spectrum generating algebras to quan- tum many-body scars, Phys. Rev. B102, 085140 (2020)

    work page 2020

  54. [54]

    D. K. Mark, C.-J. Lin, and O. I. Motrunich, Unified structure for exact towers of scar states in the affleck-kennedy-lieb-tasaki and other models, Phys. Rev. B101, 195131 (2020)

    work page 2020

  55. [55]

    The many-body localization phase transition

    A. Pal and D. A. Huse, Many-body localization phase tran- sition, Physical Review B - Condensed Matter and Materials Physics82, 1 (2010), arXiv:1010.1992

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  56. [56]

    D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Colloquium: Many-body localization, thermalization, and entanglement, Re- views of Modern Physics91, 10.1103/RevModPhys.91.021001 (2019), arXiv:1804.11065v2

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/revmodphys.91.021001 2019

  57. [57]

    Lukin, M

    A. Lukin, M. Rispoli, R. Schittko, M. E. Tai, A. M. Kauf- man, S. Choi, V . Khemani, J. L´eonard, and M. Greiner, Probing entanglement in a many-body–localized system, Science364, 256–260 (2019)

    work page 2019

  58. [58]

    Bluvstein, A

    D. Bluvstein, A. Omran, H. Levine, A. Keesling, G. Semeghini, S. Ebadi, T. T. Wang, A. A. Michailidis, N. Maskara, W. W. Ho, et al., Controlling quantum many-body dynamics in driven rydberg atom arrays, Science371, 1355 (2021)

    work page 2021

  59. [59]

    Bluvstein, H

    D. Bluvstein, H. Levine, G. Semeghini, T. T. Wang, S. Ebadi, M. Kalinowski, A. Keesling, N. Maskara, H. Pichler, M. Greiner, V . Vuleti´c, and M. D. Lukin, A quantum processor based on coherent transport of entangled atom arrays, Nature 604, 451–456 (2022)

    work page 2022

  60. [60]

    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,...

    work page 2023

  61. [61]

    Ryan-Anderson, J

    C. Ryan-Anderson, J. G. Bohnet, K. Lee, D. Gresh, A. Hankin, J. P. Gaebler, D. Francois, A. Chernoguzov, D. Lucchetti, N. C. 7 Brown, T. M. Gatterman, S. K. Halit, K. Gilmore, J. A. Gerber, B. Neyenhuis, D. Hayes, and R. P. Stutz, Realization of real- time fault-tolerant quantum error correction, Phys. Rev. X11, 041058 (2021)

    work page 2021

  62. [62]

    M. P. Fisher, V . Khemani, A. Nahum, and S. Vijay, Ran- dom Quantum Circuits, Annual Review of Condensed Matter Physics14, 335 (2023)

    work page 2023

  63. [63]

    A. C. Potter and R. Vasseur, Entanglement dynamics in hybrid quantum circuits (2021)

    work page 2021

  64. [64]

    G.-Y . Zhu, N. Tantivasadakarn, A. Vishwanath, S. Trebst, and R. Verresen, Nishimori’s Cat: Stable Long-Range Entangle- ment from Finite-Depth Unitaries and Weak Measurements, Phys. Rev. Lett.131, 200201 (2023)

    work page 2023

  65. [65]

    E. H. Chen, G.-Y . Zhu, R. Verresen, A. Seif, E. B¨aumer, D. Lay- den, N. Tantivasadakarn, G. Zhu, S. Sheldon, A. Vishwanath, S. Trebst, and A. Kandala, Nishimori transition across the error threshold for constant-depth quantum circuits, Nature Physics 21, 161 (2025)

    work page 2025

  66. [66]

    G.-Y . Zhu, N. Tantivasadakarn, and S. Trebst, Structured volume-law entanglement in an interacting, monitored majo- rana spin liquid, Phys. Rev. Res.6, L042063 (2024)

    work page 2024

  67. [67]

    Eckstein, B

    F. Eckstein, B. Han, S. Trebst, and G.-Y . Zhu, Robust Telepor- tation of a Surface Code and Cascade of Topological Quantum Phase Transitions, PRX Quantum5, 040313 (2024)

    work page 2024

  68. [68]

    P¨ utz, R

    M. P ¨utz, R. Vasseur, A. W. W. Ludwig, S. Trebst, and G.-Y . Zhu, Flow to Nishimori universality in weakly moni- tored quantum circuits with qubit loss, arXiv e-prints (2025), arXiv:2505.22720 [cond-mat.stat-mech]

    work page arXiv 2025

  69. [69]

    Q. Wang, R. Vasseur, S. Trebst, A. W. W. Ludwig, and G.-Y . Zhu, Decoherence-induced self-dual criticality in topological states of matter, preprint (2025), arXiv:2502.14034

    work page arXiv 2025

  70. [70]

    C. H. Bennett, Demons, engines and the second law, Scientific American257, 108 (1987)

    work page 1987

  71. [71]

    H. S. Leff and A. F. Rex, eds., Maxwell’s demon: entropy, information, computing (Princeton University Press, Princeton, 2014)

    work page 2014

  72. [72]

    Szilard, ¨Uber die Entropieverminderung in einem ther- modynamischen System bei Eingriffen intelligenter Wesen, Zeitschrift f¨ur Physik53, 840 (1929)

    L. Szilard, ¨Uber die Entropieverminderung in einem ther- modynamischen System bei Eingriffen intelligenter Wesen, Zeitschrift f¨ur Physik53, 840 (1929)

    work page 1929

  73. [73]

    Landauer, Irreversibility and heat generation in the comput- ing process, IBM Journal of Research and Development5, 183 (1961)

    R. Landauer, Irreversibility and heat generation in the comput- ing process, IBM Journal of Research and Development5, 183 (1961)

    work page 1961

  74. [74]

    Toyabe, T

    S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, and M. Sano, Experimental demonstration of information-to-energy conver- sion and validation of the generalized Jarzynski equality, Nature Physics6, 988 (2010)

    work page 2010

  75. [75]

    J. V . Koski, V . F. Maisi, J. P. Pekola, and D. V . Averin, Ex- perimental realization of a szilard engine with a single elec- tron, Proceedings of the National Academy of Sciences111, 13786–13789 (2014)

    work page 2014

  76. [76]

    J. P. S. Peterson, R. S. Sarthour, A. M. Souza, I. S. Oliveira, J. Goold, K. Modi, D. O. Soares-Pinto, and L. C. C´eleri, Exper- imental demonstration of information to energy conversion in a quantum system at the landauer limit, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, 20150813 (2016)

    work page 2016

  77. [77]

    Ergotropy of quantum many-body scars

    Z. Zhi, Q. Qian, J. Liu, and G.-Y . Zhu, Data for “Ergotropy of quantum many-body scars”, Zenodo 10.5281/zenodo.17864761 (2025)

    work page doi:10.5281/zenodo.17864761 2025

  78. [78]

    Ergotropy of quantum many-body scars

    Z. Zhi, Q. Qian, J. Liu, and G.-Y . Zhu, Code for “Ergotropy of quantum many-body scars” (2025)

    work page 2025

  79. [79]

    Lin and O

    C.-J. Lin and O. I. Motrunich, Exact quantum many-body scar states in the rydberg-blockaded atom chain, Phys. Rev. Lett. 122, 173401 (2019)

    work page 2019

  80. [80]

    A. N. Ivanov and O. I. Motrunich, Many exact area-law scar eigenstates in the nonintegrable pxp and related models (2025), arXiv:2503.16327 [quant-ph]

    work page arXiv 2025

Showing first 80 references.