Classical many-body chaos with and without quasiparticles

We study correlations, transport and chaos in a Heisenberg magnet as classical model many-body system. By varying temperature dimensionality, we can tune between settings with without symmetry breaking accompanying collective modes or quasiparticles. analyse both conventional out-of-time-ordered spin correlators (`decorrelators') to track the spreading of spatiotemporally localised perturbation -- wingbeat butterfly well coefficients Lyapunov exponents. identify number qualitatively different regimes. Trivially, at $T=0$, there is no dynamics all. In limit low temperature, $T=0^+$, integrability emerges, infinitely long-lived magnons; here wavepacket created by propagates ballistically, yielding lightcone wave velocity which thus subsumes velocity; inside lightcone, pattern characteristic free spectrum visible short times. On top this, residual interactionslead lifetimes which, while divergent this limit, remain finite any nonzero $T$. At longest times, leads `standard' chaotic regime; for regime, show that exponent simply proportional inverse spin-wave lifetime. Visibly strikingly, `short-time' integrable regimes, scarred regime emerges: here, decorrelator highly non-uniform, being dominated rare random scattering events seeding secondary lightcones. As correlation length decreases increasing $T$, distinction these regimes disappears high previously studied paramagnetic emerges. For elucidate how, somewhat counterintuitively, ballistic arises from diffusive dynamics.