  We consider the nonequilibrium protocol where two semi-infinite gapped XXZ
chains, initially prepared in different equilibrium states, are suddenly joint
together. At large times, a generalized hydrodynamic description applies,
according to which the system can locally be represented by space- and time-
dependent stationary states. The magnetization displays an unusual behavior:
depending on the initial state, its profile may exhibit abrupt jumps that can
not be predicted directly from the standard hydrodynamic equations and which
signal non-ballistic spin transport. We ascribe this phenomenon to the
structure of the local conservation laws and make a prediction for the exact
location of the jumps. We find that the jumps propagate at the velocities of
the heaviest quasiparticles. By means of tDMRG simulations we show that our
theory yields a complete description of the long-time steady profiles of
conserved charges, currents, and local correlations.
