  We study an open Heisenberg XXZ spin chain with long-range Ising-type
interaction, which is incoherently driven at its boundaries and therefore a
far-from-equilibrium steady state current is induced. Quantum Monte Carlo
techniques make a regime accessible, where the system size is large enough to
examine the transition from a diffusive to a ballistic transport regime. We
find that the chain lengths for this transition are increasing with decreasing
range of the Ising-type interactions between distant spins, while the strength
of the incoherent driving does not have a relevant effect on the transport
transition. The transition can be explained by the suppression of ferromagnetic
domains at the edges of the chain.
