Temperature dependence of butterfly effect in a classical many-body system

TL;DR

This paper investigates how chaos, characterized by the butterfly effect, in a classical spin system on a kagome lattice depends on temperature, revealing power-law behaviors and differences from quantum bounds.

Contribution

It provides the first detailed analysis of temperature-dependent chaos measures in a classical many-body spin system, especially in the spin liquid phase.

Findings

Chaotic dynamics persists down to zero temperature due to spin liquid phase.

Lyapunov exponent scales as T^{0.48}, slower than quantum bound.

Power-law relations between chaos measures and spin dynamics are established.

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, $D$ and spin-autocorrelation time, $\tau$. We find that they all exhibit power law behaviour at low temperature, consistent with scaling of the form $D\sim v_b^2/\mu$ and $\tau^{-1}\sim T$. 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.