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We study the dynamics of a spin-1/2 XXZ chain which is initially prepared ina domain-wall state. We compare the results of time-dependent Density MatrixRenormalization Group simulations with those of an effective description interms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerousquantities are analyzed: magnetization (x, y and z components), energy density,energy current, but also some spin-spin correlation functions or entanglemententropy in the quantum chain. Without any adjustable parameter a quantitativeagreement is observed between the quantum and the LL problems in the long timelimit, when the models are close to the isotropic point. This is explained as aconsequence of energy conservation. At the isotropic point the mapping betweenthe LL equation and the nonlinear Schr\"odinger equation is used to construct avariational solution capturing several aspects of the problem.

Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point