Many-body chaos: phase transition and noise*

Chaos is an important characterisation of classical dynamical systems. How is chaos linked to the long-time dynamics of collective modes across phases and phase transitions? We address this by studying chaos across Ising and Kosterlitz-Thouless transitions in classical XXZ model. We show that spatiotemporal chaotic properties characterized by a classical out-of-time correlation (cOTOC) function have crossovers across the transitions and distinct temperature dependence in the high and low-temperature phases which show normal and anomalous diffusion, respectively. We further show that a suitably defined cOTOC can be used in an interacting system with both noise and dissipation to characterize growth and spread of chaos, which are typically defined for deterministic dynamics, unlike the non-deterministic dynamics in the presence of random noise. We show the existence of non-chaotic to chaotic transition as a function of the ratio of interaction and noise strength.