Temperature Dependence of the Butterfly Effect in a Classical Many-Body System

We study the chaotic dynamics in a classical many-body system of interacting spins on the kagome lattice. We characterize many-body chaos via the butterfly effect as captured by an appropriate out-of-time-ordered commutator. Due to the emergence of a spin-liquid phase, the chaotic dynamics extends all the way to zero temperature. We thus determine the full temperature dependence of two complementary aspects of the butterfly effect: the Lyapunov exponent, mu, and the butterfly speed, v(b), and study their interrelations with usual measures of spin dynamics such as the spin-diffusion constant, D, and spin-autocorrelation time, tau. We find that they all exhibit power-law behavior at low temperature, consistent with scaling of the form D similar to v(b)(2)/mu and tau(-1) similar to T. The vanishing of mu similar to T-0.48 is parametrically slower than that of the corresponding quantum bound, mu similar to T, raising interesting questions regarding the semiclassical limit of such spin systems.