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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• Superdiffusion from nonabelian symmetries in nearly integrable systems
• Long-lived Solitons and Their Signatures in the Classical Heisenberg Chain
• Domain wall melting in spin-1 chains
• Exact time evolution formulae in the XXZ spin chain with domain wall initial state
• Domain wall dynamics in classical spin chains: free propagation, subdiffusive spreading, and soliton emission
• Interaction-induced transition in quantum many-body detection probability
• Domain-wall melting and entanglement in free-fermion chains with a band structure
• Nonlinear steepest descent on a torus: A case study of the Landau-Lifshitz equation
• Lindblad quantum dynamics from correlation functions of classical spin chains
• Universal scaling of higher-order cumulants in quantum isotropic spin chains