Domain-wall dynamics in the Landau-Lifshitz magnet and the classical-quantum correspondence for spin transport

We investigate the dynamics of spin in the axially anisotropic Landau-Lifshitz field theory with a magnetic domain-wall initial condition. Employing the analytic scattering technique, we obtain the exact scattering data and reconstruct the time-evolved profile. We identify three qualitatively distinct regimes of spin transport, ranging from ballistic expansion in the easy-plane regime, absence of transport in the easy-axis regime, and logarithmically enhanced diffusion for the isotropic interaction. Our results are in perfect qualitative agreement with those found in the anisotropic quantum Heisenberg spin-1/2 chain, indicating a remarkable classical-quantum correspondence for macroscopic spin transport.