  Recent studies report on anomalous spin transport for the integrable
Heisenberg spin chain at its isotropic point. Anomalous scaling is also
observed in the time-evolution of non-equilibrium initial conditions, the decay
of current-current correlations, and non-equilibrium steady state averages.
These studies indicate a space-time scaling with $x \sim t^{2/3}$ behavior at
the isotropic point, in sharp contrast to the ballistic form $x \sim t$
generically expected for integrable systems. In our contribution we study the
scaling behavior for the integrable lattice Landau-Lifshitz spin chain. We
report on equilibrium spatio-temporal correlations and dynamics with step
initial conditions. Remarkably, for the case with zero mean magnetization, we
find strong evidence that the scaling function is identical to the one obtained
from the stationary stochastic Burgers equation, alias Kardar-Parisi-Zhang
equation. In addition, we present results for the easy-plane and easy-axis
regimes for which, respectively, ballistic and diffusive spin transport is
observed, whereas the energy remains ballistic over the entire parameter
regime.
