Temperature dependence of 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 characterise 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, μ, and the butterfly speed, vb, and study their interrelations with usual measures of spin dynamics such as the spin-diffusion constant, D and spin-autocorrelation time, τ. We find that they all exhibit power law behaviour at low temperature, consistent with scaling of the form D∼v_b²/μ and τ^-1−T. The vanishing of μ∼T^0.48 is parametrically slower than that of the corresponding quantum bound, μ∼T, raising interesting questions regarding the semi-classical limit of such spin systems.