Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions

Sibaram Ruidas, Sumilan Banerjee

Published 2020-07-24Version 1

Chaos, the sensitivity to initial conditions, is an important tool to classify intermediate-time behaviour of classical dynamical systems. On the other hand, the long-time dynamical properties of interacting many-body systems, in symmetry broken and unbroken phases, and across phase transitions, are often characterized by the properties of the collective low-energy excitations, hydrodynamic and critical modes. How are the short-time chaotic properties of classical many-body systems related to their long-time dynamics? Can the phases and phase transitions be classified in terms of chaos? We address these questions by studying the temperature dependence of the chaos across two paradigmatic thermal phase transitions in two-dimensional anisotropic XXZ model, which has an intrinsic spin precession dynamics in the classical limit. We tune the phase transition from the Kosterlitz-Thouless (KT) to Ising universality class by changing the anisotropy and find the temperature dependence of the growth rate of chaos, the Lyapunov exponent ${\lambda}_\mathrm{L}$, and the velocity $v_B$ of ballistic spread of a local perturbation. For both the KT and Ising transitions, we find no strong effect of critical slowing down, only a crossover in $\lambda_\mathrm{L}$ and a dip in $v_B$ at the transitions, with distinct temperature dependences in the high and low-temperature phases. We argue that the ballistic spread of chaos can be connected with diffusion at high temperature. However, no such correlation exists for the low temperature phases, which exhibit anomalous diffusion, and where the chaos originates from weak interactions between low-energy excitations, namely the spin-waves.