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arxiv: 2208.13767 · v3 · pith:PGNPZDE5new · submitted 2022-08-29 · ❄️ cond-mat.stat-mech · cond-mat.str-el· hep-th· quant-ph

Hot band sound

Vir B. Bulchandani , David A. Huse This is my paper

Pith reviewed 2026-05-24 11:23 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.str-elhep-thquant-ph
keywords hot band soundchaotic fermionsinfinite temperaturelong-range interactionsunderdamped transportspinless fermion chainsdensity waves
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0 comments X

The pith

Tuning long-range interactions in chaotic fermion chains produces underdamped hot band sound at infinite temperature.

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

Chaotic lattice models at high temperature are expected to show only diffusive transport of conserved charges, with overdamped relaxation of currents. The paper demonstrates that one-dimensional spinless fermion chains with long-range density-density interactions can be tuned to cross over to an underdamped regime where sound waves of charge density propagate with arbitrarily long damping times. This occurs while an effective interaction strength remains fixed, and the models stay chaotic and non-integrable. The result holds at infinite temperature and within a single band.

Core claim

By appropriately tuning the inter-particle interactions, lattice models of chaotic fermions at infinite temperature can be made to cross over from an overdamped regime of diffusion to an underdamped regime of hot band sound. In a family of one-dimensional spinless fermion chains with long-range density-density interactions, the damping time of sound waves can be made arbitrarily long even as an effective interaction strength is held fixed.

What carries the argument

Long-range density-density interactions in one-dimensional spinless fermion chains, which allow the sound damping time to be extended arbitrarily at fixed effective interaction strength while preserving chaos.

Load-bearing premise

The models remain chaotic and non-integrable while the interaction range is tuned to make the sound damping time arbitrarily long at fixed effective interaction strength.

What would settle it

Numerical or experimental observation that increasing the interaction range in these fermion chains either fails to extend the sound damping time or causes the system to lose chaotic behavior.

Figures

Figures reproduced from arXiv: 2208.13767 by David A. Huse, Vir B. Bulchandani.

Figure 1
Figure 1. Figure 1: FIG. 1. Decay of an initial density modulation in a system of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Numerical evaluation of the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Chaotic lattice models at high temperature are generically expected to exhibit diffusive transport of all local conserved charges. Such diffusive transport is usually associated with overdamped relaxation of the associated currents. Here we show that by appropriately tuning the inter-particle interactions, lattice models of chaotic fermions at infinite temperature can be made to cross over from an overdamped regime of diffusion to an underdamped regime of ``hot band sound''. We study a family of one-dimensional spinless fermion chains with long-range density-density interactions, in which the damping time of sound waves can be made arbitrarily long even as an effective interaction strength is held fixed. Our results demonstrate that underdamped sound waves of charge density can arise within a single band, with strong interactions and far from integrability, and at very high temperature.

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

1 major / 2 minor

Summary. The manuscript introduces a family of one-dimensional spinless fermion chains with tunable long-range density-density interactions at infinite temperature. It claims that increasing the interaction range (while holding an effective interaction strength fixed) produces a crossover from overdamped diffusive transport to underdamped 'hot band sound' propagation of charge density, with the sound damping time made arbitrarily long, all while the models remain chaotic and non-integrable.

Significance. If the central claim holds, the result is significant: it would demonstrate that underdamped collective modes of a conserved charge can emerge inside a single band, at strong coupling and infinite temperature, without integrability or additional bands. This challenges the generic expectation of purely diffusive transport in chaotic many-body systems and supplies concrete lattice models for further study.

major comments (1)
  1. [§3] The load-bearing assumption is that non-integrability and chaos persist as the interaction range is increased to make the damping time diverge at fixed effective strength. §3 (or the equivalent model-definition section) and the associated numerics must explicitly demonstrate that the largest Lyapunov exponent (or equivalent chaos diagnostic) remains positive and does not approach zero in the long-range limit used for the underdamped regime; without this, the crossover could occur outside the claimed chaotic setting.
minor comments (2)
  1. [Fig. 2] Figure captions should state the precise definition of the effective interaction strength that is held fixed when the range is varied.
  2. [§4] The abstract states the damping time 'can be made arbitrarily long'; the main text should quantify the scaling of the damping time with the range parameter and show the data collapse or fit that supports this statement.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive assessment of the significance of our work and for the constructive major comment. We address the point below.

read point-by-point responses

  1. Referee: [§3] The load-bearing assumption is that non-integrability and chaos persist as the interaction range is increased to make the damping time diverge at fixed effective strength. §3 (or the equivalent model-definition section) and the associated numerics must explicitly demonstrate that the largest Lyapunov exponent (or equivalent chaos diagnostic) remains positive and does not approach zero in the long-range limit used for the underdamped regime; without this, the crossover could occur outside the claimed chaotic setting.

    Authors: We agree that an explicit demonstration of persistent chaos is required to substantiate the central claim. The original manuscript supported non-integrability via level repulsion in the many-body spectrum and the absence of extra conserved quantities. To directly meet the referee's request, the revised manuscript will add, in §3, numerical results for the largest Lyapunov exponent (computed via the classical limit or an equivalent quantum diagnostic such as the growth rate of out-of-time-order correlators) at the long-range parameters realizing the underdamped regime. These data will show that the exponent remains positive and does not approach zero when the interaction range is increased at fixed effective strength, confirming that the crossover occurs inside the chaotic phase. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper defines a family of long-range interacting fermion chains, tunes the interaction range while holding an effective strength fixed, and reports that the sound damping time diverges while the model remains chaotic. No step reduces a claimed prediction to a fitted parameter by construction, no self-citation is invoked as a uniqueness theorem or load-bearing premise, and no ansatz is smuggled in. The central result is obtained by direct study of the defined models rather than by re-labeling inputs; the skeptic concern about hidden integrability is a question of model validity, not a circular reduction in the derivation chain itself.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no explicit free parameters, axioms, or invented entities can be extracted. The tuning of interaction range is the operative choice but cannot be classified without the model definition.

pith-pipeline@v0.9.0 · 5662 in / 1065 out tokens · 19591 ms · 2026-05-24T11:23:55.406555+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

28 extracted references · 28 canonical work pages · 1 internal anchor

  1. [1]

    V. J. Emery and S. A. Kivelson, Phys. Rev. Lett. 74, 3253 (1995)

    work page 1995

  2. [2]

    Gunnarsson, M

    O. Gunnarsson, M. Calandra, and J. E. Han, Rev. Mod. Phys. 75, 1085 (2003)

    work page 2003

  3. [3]

    N. E. Hussey, K. Takenaka, and H. Tak- agi, Philosophical Magazine 84, 2847 (2004), https://doi.org/10.1080/14786430410001716944

    work page doi:10.1080/14786430410001716944 2004

  4. [4]

    S. A. Hartnoll and A. P. Mackenzie, Planckian dissipation in metals (2021), arXiv:2107.07802

    work page arXiv 2021

  5. [5]

    P. W. Phillips, N. E. Hussey, and P. Ab- bamonte, Science 377, eabh4273 (2022), https://www.science.org/doi/pdf/10.1126/science.abh4273

    work page doi:10.1126/science.abh4273 2022

  6. [6]

    P. T. Brown, D. Mitra, E. Guardado-Sanchez, R. Nourafkan, A. Reymbaut, C.-D. H´ ebert, S. Berg- eron, A.-M. S. Tremblay, J. Kokalj, D. A. Huse, P. Schauß, and W. S. Bakr, Science 363, 379 (2019), https://www.science.org/doi/pdf/10.1126/science.aat4134

    work page doi:10.1126/science.aat4134 2019

  7. [7]

    Zotos, F

    X. Zotos, F. Naef, and P. Prelovsek, Physical Review B 55, 11029 (1997)

    work page 1997

  8. [8]

    ˇZnidariˇ c, Phys

    M. ˇZnidariˇ c, Phys. Rev. Lett.106, 220601 (2011)

    work page 2011

  9. [9]

    Ilievski, J

    E. Ilievski, J. De Nardis, M. Medenjak, and T. Prosen, Phys. Rev. Lett. 121, 230602 (2018)

    work page 2018

  10. [10]

    Agrawal, S

    U. Agrawal, S. Gopalakrishnan, R. Vasseur, and B. Ware, Physical Review B 101, 224415 (2020)

    work page 2020

  11. [11]

    Scheie, N

    A. Scheie, N. Sherman, M. Dupont, S. Nagler, M. Stone, G. Granroth, J. Moore, and D. Tennant, Nature Physics 17, 726 (2021)

    work page 2021

  12. [12]

    D. Wei, A. Rubio-Abadal, B. Ye, F. Machado, J. Kemp, K. Srakaew, S. Hollerith, J. Rui, S. Gopalakrishnan, N. Y. Yao, I. Bloch, and J. Zeiher, Science 376, 716 (2022), https://www.science.org/doi/pdf/10.1126/science.abk2397

    work page doi:10.1126/science.abk2397 2022

  13. [13]

    V. B. Bulchandani, S. Gopalakrishnan, and E. Ilievski, Journal of Statistical Mechanics: Theory and Experi- ment 2021, 084001 (2021)

    work page 2021

  14. [14]

    V. B. Bulchandani, C. Karrasch, and J. E. Moore, Pro- ceedings of the National Academy of Sciences 117, 12713 (2020)

    work page 2020

  15. [15]

    O. A. Castro-Alvaredo, B. Doyon, and T. Yoshimura, Phys. Rev. X 6, 041065 (2016)

    work page 2016

  16. [16]

    Bertini, M

    B. Bertini, M. Collura, J. De Nardis, and M. Fagotti, Phys. Rev. Lett. 117, 207201 (2016)

    work page 2016

  17. [17]

    V. B. Bulchandani, R. Vasseur, C. Karrasch, and J. E. Moore, Physical Review B 97, 10.1103/Phys- RevB.97.045407 (2018), arXiv:1702.06146

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/phys- 2018

  18. [18]

    Doyon, T

    B. Doyon, T. Yoshimura, and J.-S. Caux, Phys. Rev. Lett. 120, 045301 (2018)

    work page 2018

  19. [19]

    Bastianello, J

    A. Bastianello, J. De Nardis, and A. De Luca, Phys. Rev. B 102, 161110 (2020)

    work page 2020

  20. [20]

    E. M. Lifshitz and L. P. Pitaevskii, Statistical physics: theory of the condensed state , Vol. 9 (Elsevier, 2013)

    work page 2013

  21. [21]

    This model in fact exhibits superdiffusive charge transport8,9,11–13. Tuning the effective XXZ anisotropy ∆ = U1 of the integrable reference point in our con- strained optimization problem is equivalent to tuning the value of the interaction constraint σ2 V . We have checked that even when σ2 V/L < 1/4, which corresponds to an anisotropy|∆| < 1 and hence ba...

    work page

  22. [22]

    See Supplementary Material for a derivation

    work page

  23. [23]

    Oganesyan and D

    V. Oganesyan and D. A. Huse, Phys. Rev. B 75, 155111 (2007)

    work page 2007

  24. [24]

    V. B. Bulchandani and D. A. Huse, in preparation

    work page

  25. [25]

    Mierzejewski, J

    M. Mierzejewski, J. Wronowicz, and J. Herbrych, Quasi- ballistic transport within long-range anisotropic heisen- berg model (2022), arXiv:2206.05960

    work page arXiv 2022

  26. [26]

    Monroe, W

    C. Monroe, W. C. Campbell, L.-M. Duan, Z.-X. Gong, A. V. Gorshkov, P. W. Hess, R. Islam, K. Kim, N. M. Linke, G. Pagano, P. Richerme, C. Senko, and N. Y. Yao, 6 Rev. Mod. Phys. 93, 025001 (2021)

    work page 2021

  27. [27]

    Korenblit, D

    S. Korenblit, D. Kafri, W. C. Campbell, R. Islam, E. E. Edwards, Z.-X. Gong, G.-D. Lin, L.-M. Duan, J. Kim, K. Kim, and C. Monroe, New Journal of Physics 14, 095024 (2012)

    work page 2012

  28. [28]

    square root

    L. Erd˝ os, M. Salmhofer, and H.-T. Yau, Journal of Sta- tistical Physics 116, 367 (2004). Quantum Boltzmann equation for hot band sound In this Appendix, we argue that the dynamics of optimal models forR≫ 1 and infinite temperature is approximated by a linearized Boltzmann equation of the form ∂tδρk +vk∂xδρk =D∂2 kδρk, (26) where the effective pseudomoment...

    work page 2004