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Emergence of many-body chaos in the presence of quasiparticles

Sibaram Ruidas1,*, Sthitadhi Roy1,2,†, Subhro Bhattacharjee1,2,‡, and Roderich Moessner2,§

  • *Contact author: sibaram.ruidas@icts.res.in
  • †Contact author: sthitadhi.roy@icts.res.in
  • ‡Contact author: subhro@icts.res.in
  • §Contact author: moessner@pks.mpg.de
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Phys. Rev. B 114, 014306 – Published 10 July, 2026

DOI: https://doi.org/10.1103/zkvh-dqqp

Abstract

Many-body chaos is a default property of many-body systems; at the same time, near-integrable behavior due to weakly interacting quasiparticles is ubiquitous throughout condensed matter at low temperature. There must therefore be a, possibly generic, crossover between these very different regimes. Here, we develop a theory encapsulating the notion of a cascade of lightcones seeded by sequences of scattering of weakly interacting harmonic modes as witnessed by a suitably defined chaos diagnostic (classical decorrelator) that measures the spatiotemporal profile of many-body chaos. Our numerics deals with the concrete prototypical case of a classical Heisenberg chain, for either sign of the interaction, at low temperatures where the short-time dynamics are well captured in terms of noninteracting spin waves—characteristic to continuous symmetry breaking. To model low-temperature dynamics, we use ensembles of initial states with randomly embedded point defects in an ordered background, which provides a controlled setting for studying the scattering events. The decorrelator exhibits a short-time integrable regime followed by an intermediate “scarred” regime of the cascade of lightcones in progress; these then overlap, leading to an avalanche of scattering events which finally yields the standard long-time signature of many-body chaos.

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References (61)

  1. A. S. Pikovsky and J. Kurths, Roughening interfaces in the dynamics of perturbations of spatiotemporal chaos, Phys. Rev. E 49, 898 (1994).
  2. P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, UK, 2000)
  3. R. Livi, A. Politi, and S. Ruffo, Distribution of characteristic exponents in the thermodynamic limit, J. Phys. A: Math. Gen. 19, 2033 (1986).
  4. M. Cencini and A. Torcini, Linear and nonlinear information flow in spatially extended systems, Phys. Rev. E 63, 056201 (2001).
  5. J. A. Vastano and H. L. Swinney, Information transport in spatiotemporal systems, Phys. Rev. Lett. 60, 1773 (1988).
  6. S. Lepri, A. Politi, and A. Torcini, Chronotopic Lyapunov analysis. I. A detailed characterization of 1D systems, J. Stat. Phys. 82, 1429 (1996).
  7. S. Lepri, A. Politi, and A. Torcini, Chronotopic Lyapunov analysis: II. Toward a unified approach, J. Stat. Phys. 88, 31 (1997).
  8. G. Giacomelli, R. Hegger, A. Politi, and M. Vassalli, Convective Lyapunov exponents and propagation of correlations, Phys. Rev. Lett. 85, 3616 (2000).
  9. I. L. Aleiner, L. Faoro, and L. B. Ioffe, Microscopic model of quantum butterfly effect: Out-of-time-order correlators and traveling combustion waves, Ann. Phys. (NY) 375, 378 (2016).
  10. S. H. Shenker and D. Stanford, Black holes and the butterfly effect, J. High Energy Phys. 03 (2014) 067.
  11. J. Maldacena, S. H. Shenker, and D. Stanford, A bound on chaos, J. High Energy Phys. 08 (2016) 106.
  12. A. Bohrdt, C. B. Mendl, M. Endres, and M. Knap, Scrambling and thermalization in a diffusive quantum many-body system, New J. Phys. 19, 063001 (2017).
  13. D. J. Luitz and Y. B. Lev, Information propagation in isolated quantum systems, Phys. Rev. B 96, 020406(R) (2017).
  14. E. B. Rozenbaum, S. Ganeshan, and V. Galitski, Lyapunov exponent and out-of-time-ordered correlator's growth rate in a chaotic system, Phys. Rev. Lett. 118, 086801 (2017).
  15. P. Hosur, X.-L. Qi, D. A. Roberts, and B. Yoshida, Chaos in quantum channels, J. High Energy Phys. 02 (2016) 004.
  16. J. Kurchan, Quantum bound to chaos and the semiclassical limit, J. Stat. Phys. 171, 965 (2018).
  17. D. A. Roberts and B. Swingle, Lieb-Robinson bound and the butterfly effect in quantum field theories, Phys. Rev. Lett. 117, 091602 (2016).
  18. A. Das, S. Chakrabarty, A. Dhar, A. Kundu, D. A. Huse, R. Moessner, S. S. Ray, and S. Bhattacharjee, Light-cone spreading of perturbations and the butterfly effect in a classical spin chain, Phys. Rev. Lett. 121, 024101 (2018).
  19. T. Bilitewski, S. Bhattacharjee, and R. Moessner, Temperature dependence of the butterfly effect in a classical many-body system, Phys. Rev. Lett. 121, 250602 (2018).
  20. T. Bilitewski, S. Bhattacharjee, and R. Moessner, Classical many-body chaos with and without quasiparticles, Phys. Rev. B 103, 174302 (2021).
  21. S. Ruidas and S. Banerjee, Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions, SciPost Phys. 11, 087 (2021).
  22. S. D. Murugan, D. Kumar, S. Bhattacharjee, and S. S. Ray, Many-body chaos in thermalized fluids, Phys. Rev. Lett. 127, 124501 (2021).
  23. A. Banerjee, R. Mukherjee, S. D. Murugan, S. Bhattacharjee, and S. S. Ray, Intermittent fluctuations determine the nature of chaos in turbulence, Phys. Rev. Lett. 136, 214001 (2026).
  24. B. V. Fine, T. A. Elsayed, C. M. Kropf, and A. S. de Wijn, Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2, Phys. Rev. E 89, 012923 (2014).
  25. D. Métivier, R. Bachelard, and M. Kastner, Spreading of perturbations in long-range interacting classical lattice models, Phys. Rev. Lett. 112, 210601 (2014).
  26. E. Iyoda and T. Sagawa, Scrambling of quantum information in quantum many-body systems, Phys. Rev. A 97, 042330 (2018).
  27. B. Swingle and D. Chowdhury, Slow scrambling in disordered quantum systems, Phys. Rev. B 95, 060201(R) (2017).
  28. S. Banerjee and E. Altman, Solvable model for a dynamical quantum phase transition from fast to slow scrambling, Phys. Rev. B 95, 134302 (2017).
  29. T. Scaffidi and E. Altman, Chaos in a classical limit of the Sachdev-Ye-Kitaev model, Phys. Rev. B 100, 155128 (2019).
  30. A. A. Patel, D. Chowdhury, S. Sachdev, and B. Swingle, Quantum butterfly effect in weakly interacting diffusive metals, Phys. Rev. X 7, 031047 (2017).
  31. A. A. Patel and S. Sachdev, Quantum chaos on a critical Fermi surface, Proc. Natl. Acad. Sci. USA 114, 1844 (2017).
  32. V. Khemani, A. Vishwanath, and D. A. Huse, Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws, Phys. Rev. X 8, 031057 (2018).
  33. T. Rakovszky, F. Pollmann, and C. W. von Keyserlingk, Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation, Phys. Rev. X 8, 031058 (2018).
  34. C. W. von Keyserlingk, T. Rakovszky, F. Pollmann, and S. L. Sondhi, Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws, Phys. Rev. X 8, 021013 (2018).
  35. A. Nahum, S. Vijay, and J. Haah, Operator spreading in random unitary circuits, Phys. Rev. X 8, 021014 (2018).
  36. C.-J. Lin and O. I. Motrunich, Out-of-time-ordered correlators in a quantum Ising chain, Phys. Rev. B 97, 144304 (2018).
  37. B. Dóra and R. Moessner, Out-of-time-ordered density correlators in Luttinger liquids, Phys. Rev. Lett. 119, 026802 (2017).
  38. A. Schuckert and M. Knap, Many-body chaos near a thermal phase transition, SciPost Phys. 7, 022 (2019).
  39. A. S. de Wijn, B. Hess, and B. V. Fine, Lyapunov instabilities in lattices of interacting classical spins at infinite temperature, J. Phys. A: Math. Theor. 46, 254012 (2013).
  40. A. S. de Wijn, B. Hess, and B. V. Fine, Largest Lyapunov exponents for lattices of interacting classical spins, Phys. Rev. Lett. 109, 034101 (2012).
  41. J. Kim, X. Cao, and E. Altman, Scrambling versus relaxation in Fermi and non-Fermi liquids, Phys. Rev. B 102, 085134 (2020).
  42. S. Xu and B. Swingle, Locality, quantum fluctuations, and scrambling, Phys. Rev. X 9, 031048 (2019).
  43. A. Deger, S. Roy, and A. Lazarides, Arresting classical many-body chaos by kinetic constraints, Phys. Rev. Lett. 129, 160601 (2022).
  44. S. Ruidas and S. Banerjee, Semiclassical limit of a measurement-induced transition in many-body chaos in integrable and nonintegrable oscillator chains, Phys. Rev. Lett. 132, 030402 (2024).
  45. A. I. Larkin and Y. N. Ovchinnikov, Quasiclassical method in the theory of superconductivity, Sov. Phys. JETP 28, 1200 (1969).
  46. A. Y. Kitaev, KITP program on entanglement in strongly-correlated quantum matter, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 2015, https://online.kitp.ucsb.edu/seminars/entangled15-all.html.
  47. E. N. Lorenz, The Essence of Chaos (University of Washington Press, Seattle, WA, 1993).
  48. R. C. Hilborn, Sea gulls, butterflies, and grasshoppers: A brief history of the butterfly effect in nonlinear dynamics, Am. J. Phys. 72, 425 (2004).
  49. P. Gaspard, Chaos, Scattering and Statistical Mechanics, Cambridge Nonlinear Science Series (Cambridge University Press, Cambridge, UK, 1998).
  50. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics (Springer Science & Business Media, Cham, 2013), Vol. 38.
  51. H. G. Schuster and W. Just, Deterministic Chaos: An Introduction (Wiley Online Library, 1988), Vol. 2.
  52. K. Kaneko and I. Tsuda, Complex Systems: Chaos and Beyond: A Constructive Approach with Applications in Life Sciences (Springer Science & Business Media, Cham, 2011).
  53. M. Van Dyke, An Album of Fluid Motion (Parabolic Press, Stanford, CA, 1982).
  54. D. Chowdhury and B. Swingle, Onset of many-body chaos in the O(N) model, Phys. Rev. D 96, 065005 (2017).
  55. M. Ausloos, The Logistic Map and the Route to Chaos: From the Beginnings to Modern Applications (Springer Science & Business Media, Cham, 2006).
  56. D. Pines, Theory Of Quantum Liquids: Normal Fermi Liquids, 1st ed. (CRC Press, Boca Raton, 2018).
  57. V. Khemani, D. A. Huse, and A. Nahum, Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos, Phys. Rev. B 98, 144304 (2018).
  58. F. Evers and A. D. Mirlin, Anderson transitions, Rev. Mod. Phys. 80, 1355 (2008).
  59. V. Tikhomirov, Selected Works of A. N. Kolmogorov (Springer, Berlin, 1991), pp. 242–270.
  60. M. E. Fisher, Magnetism in one-dimensional systems—The Heisenberg model for infinite spin, Am. J. Phys. 32, 343 (1964).
  61. R. W. Gerling and D. P. Landau, Time-dependent behavior of classical spin chains at infinite temperature, Phys. Rev. B 42, 8214 (1990).

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Phys. Rev. B 114, 014306– Published 10 July, 2026
  • Received 2 February 2026
  • Revised 20 June 2026
  • Accepted 24 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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