  We revisit the out-of-equilibrium physics arising during the unitary
evolution of a one-dimensional XXZ spin chain initially prepared in a domain
wall state $\vert\psi_0\rangle=\vert\dots
\uparrow\uparrow\downarrow\downarrow\dots\rangle$. In absence of interactions,
we review the exact lattice calculation of several conserved quantities,
including e.g. the magnetization and the spin current profiles. At large
distances $x$ and times $t$, we show how these quantities allow for a ballistic
scaling behavior in terms of the scaling variable $\zeta= x/t$, with exactly
computable scaling functions. In such a limit of large space-time scales, we
show that the asymptotic behavior of the system is suitably captured by the
local occupation function of spinless fermionic modes, whose semi-classical
evolution in phase space is given by a Euler hydrodynamic equation. Similarly,
analytical results for the asymptotic fronts dynamics are obtained for the
interacting chain via Generalized Hydrodynamics. In the last part of the work,
we include large-scale quantum fluctuations on top of the semi-classical
hydrodynamic background in the form of a conformal field theory that lives
along the evolving Fermi contour. With this procedure, dubbed quantum
generalized hydrodynamics, it is possible to obtain exact asymptotic results
for the entanglement spreading during the melting dynamics.
