Transport in a family of rotationally-invariant classical field theories

The emergence of Kardar-Parisi-Zhang (KPZ) scaling in transport in integrable spin chains is a puzzling problem of nonequilibrium dynamics. In the past decade, there has been significant progress about its characterization, but the precise conditions and mechanisms of its appearance are only partially understood. We study to what extent the KPZ physics survives in a continuous Landau-Lifshitz (LL) field theory when it is discretized in numerical simulations (which breaks its integrability) and in a broader family of related non-integrable models. We introduce a finite temperature ensemble that tunes lattice discretization effects. We find that temperature sets a characteristic time scale below which superdiffusive spin transport and the KPZ scaling function emerges (in both in the LL theory and its nonintegrable variants). At lower temperatures, we also observe ballistic energy transport in both cases. These results suggest that lowering the temperature drives the models toward integrable points with quasi-particles excitations, thereby opening a finite time window in which KPZ physics appears even away from strict integrability.