Boundary driven Heisenberg-chain in the long-range interacting regime: Robustness against far from equilibrium effects

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.