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

Abstract

We study the chaotic dynamics in a classical many-body system of interacting spins on the kagome lattice. We characterise many-body chaos via the butterfly effect as captured by an appropriate out-of-time-ordered correlator. 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, Dand spin-autocorrelation time, \tau We find that they all exhibit power law behaviour at low temperature, consistent with scaling of the form D\sim v_b^2/\muand \tau^{-1}\sim T The vanishing of \mu\sim T^{0.48}is parametrically slower than that of the corresponding quantum bound, \mu\sim T raising interesting questions regarding the semi-classical limit of such spin systems.