  We study the dynamics of an isotropic spin-1/2 Heisenberg chain starting in a
domain-wall initial condition, where the spins are initially up on the left
half-line and down on the right half-line. We focus on the long-time behavior
of the magnetization profile. We perform extensive time-dependent
density-matrix renormalization group simulations (up to t=350) and find that
the data are compatible with a diffusive behavior. Subleading corrections decay
slowly blurring the emergence of the diffusive behavior. We also compare our
results with two alternative scenarios: superdiffusive behavior and enhanced
diffusion with a logarithmic correction. We finally discuss the evolution of
the entanglement entropy.
