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

Abstract

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 log-modified 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.

6 pages, 3 figures

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Cited by in corpus (4)

• Kardar-Parisi-Zhang universality from soft gauge modes
• Free fermions at the edge of interacting systems
• Domain wall melting in spin-1 chains
• Exact time evolution formulae in the XXZ spin chain with domain wall initial state