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Classical many-body chaos with and without quasiparticles

Thomas Bilitewski, Subhro Bhattacharjee, and Roderich Moessner
Phys. Rev. B 103, 174302 – Published 7 May 2021

Abstract

We study correlations, transport, and chaos in a Heisenberg magnet as a classical model many-body system. By varying temperature and dimensionality, we can tune between settings with and without symmetry breaking and accompanying collective modes or quasiparticles (spin waves) which in the limit of low temperatures become increasingly long-lived. Changing the sign of the exchange interaction from a ferro- to an antiferromagnetic one varies the spin-wave spectrum, and hence the low-energy spectral density. We analyze both conventional and out-of-time-ordered spin correlators (decorrelators) to track the spreading of a spatiotemporally localized perturbation—the wing beat of the butterfly—as well as transport coefficients and Lyapunov exponents. We identify a number of qualitatively different regimes. Trivially, at T=0, there is no dynamics at all. In the limit of low temperature, T=0+, integrability emerges, with infinitely long-lived magnons; here the wave packet created by the perturbation propagates ballistically, yielding a light cone at the spin-wave velocity which thus subsumes the butterfly velocity; inside the light cone, a pattern characteristic of the free spin-wave spectrum is visible at short times. On top of this, residual interactions (nonlinearities in the equations of motion) lead to spin-wave lifetimes which, while divergent in this limit, remain finite at any nonzero T. At the longest times, this leads to a standard chaotic regime; for this regime, we show that the Lyapunov exponent is simply proportional to the (inverse) spin-wave lifetime. Visibly strikingly, between this and the short-time integrable regimes, a scarred regime emerges: Here, the decorrelator is spatiotemporally highly nonuniform, being dominated by rare and random scattering events seeding secondary light cones. As the spin correlation length decreases with increasing T, the distinction between these regimes disappears and at high temperature the previously studied chaotic paramagnetic regime emerges. For this, we elucidate how, somewhat counterintuitively, the ballistic butterfly velocity arises from a diffusive spin dynamics.

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  • Received 11 November 2020
  • Revised 1 March 2021
  • Accepted 27 April 2021

DOI:https://doi.org/10.1103/PhysRevB.103.174302

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 the Max Planck Society.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Thomas Bilitewski1,2,3,*, Subhro Bhattacharjee4,†, and Roderich Moessner3,‡

  • 1JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
  • 2Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
  • 3Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
  • 4International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India

  • *thomas.bilitewski@colorado.edu
  • subhro@icts.res.in
  • moessner@pks.mpg.de

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Vol. 103, Iss. 17 — 1 May 2021

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