  We investigate the influence of different interaction strengths and
dimerizations on the magnetization transport in antiferromagnetic spin-1/2
XXZ-chains. We focus on the real-time evolution of the inhomogeneous initial
state with all spins pointing up along the z axis in the left half and down in
the right half of the chain, using the adaptive time-dependent density-matrix
renormalization group (adaptive t-DMRG). We find on time-scales accessible to
us ballistic magnetization transport for small Sz-Sz-interaction and arbitrary
dimerization, but almost no transport for stronger Sz-Sz-interaction, with a
sharp crossover at Jz=1. At Jz=1 results indicate superdiffusive transport.
Additionally, we perform a detailed analysis of the error made by the adaptive
time-dependent DMRG using the fact that the evolution in the XX-model is known
exactly. We find that the error at small times is dominated by the error made
by the Trotter decomposition, whereas for longer times the DMRG truncation
error becomes the most important, with a very sharp crossover at some "runaway"
time.
