  We investigate the Heisenberg XXZ-chain with long-range interactions in the
Z-dimension. By applying two magnetic boundary reservoirs we drive the system
out of equilibrium and induce a non-zero steady state current. The long-range
coupled chain shows nearly ballistic transport and linear response for all
potential differences of the external reservoirs. In contrast, the common
isotropic nearest-neighbor coupling shows negative differential conductivity
and a transition from diffusive to subdiffusive transport for a far from
equilibrium driving. Adding disorder, the change in the transport for nearest
neighbor coupling is therefore highly dependent on the driving. We find for the
disordered long-range coupled XXZ-chain, any change in the transport behavior
is independent of the potential difference and the coupling strengths of the
external reservoirs.
