  We study the melting of domain walls in the ferromagnetic phase of the
transverse Ising chain, created by flipping the order-parameter spins along
one-half of the chain. If the initial state is excited by a local operator in
terms of Jordan-Wigner fermions, the resulting longitudinal magnetization
profiles have a universal character. Namely, after proper rescalings, the
profiles in the noncritical Ising chain become identical to those obtained for
a critical free-fermion chain starting from a step-like initial state. The
relation holds exactly in the entire ferromagnetic phase of the Ising chain and
can even be extended to the zero-field XY model by a duality argument. In
contrast, for domain-wall excitations that are highly non-local in the
fermionic variables, the universality of the magnetization profiles is lost.
Nevertheless, for both cases we observe that the entanglement entropy
asymptotically saturates at the ground-state value, suggesting a simple form of
the steady state.
