Temperature dependence of 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, $μ$, 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, $τ$. We find that they all exhibit power law behaviour at low temperature, consistent with scaling of the form $D\sim v_b^2/μ$ and $τ^{-1}\sim T$. The vanishing of $μ\sim T^{0.48}$ is parametrically slower than that of the corresponding quantum bound, $μ\sim T$, raising interesting questions regarding the semi-classical limit of such spin systems.

6+4 pages, 4+8 figures, ancillary files include videos of the dynamics