H.Kim: Confined and deconfined chaos in classical spin systems

Nearly-integrable many-body systems occur regularly in nature and in engineered experiments. They form a physically relevant setting for the study of thermalization and chaos, both in the quantum and classical settings. A conventional characterization of chaos in such systems is their sensitivity to initial conditions, as measured by Lyapunov exponents. However, it has been recognized that this notion of chaos is not relevant to the system’s long-time stability and thermalization—a system may retain memory of quasi-conserved quantities well after initially-nearby trajectories have significantly diverged. This scenario is known in the literature as confined chaos. We numerically confirm that a slightly perturbed Ishimori spin chain—a classic example of a local integrable system—exhibits confined chaos. However, in a perturbed central spin model with XX interactions—the superintegrability of which we establish analytically—we find a completely different scenario of deconfined chaos. It is characterized by a single timescale, which describes both the Lyapunov instabilities and thermalization. We find that the thermalization happens on the fastest possible timescale. In this scenario, phase space is highly inhomogeneous, containing a finite density of unstable regions where phase space trajectories rapidly and unpredictably change their behaviors, leading to both chaos and thermalization. In both scenarios, we show that decay of quasi-conserved quantities is universal and characterized by a single timescale.