Spin transport in a Lindblad-driven isotropic quantum Heisenberg spin-chain

We investigate the spin transport properties of an isotropic quantum Heisenberg spin-chain. Driving the system out of equilibrium via two different reservoirs at the boundaries, the system exhibits negative differential conductivity for strong driving. We describe the system-reservoir interaction with a Lindblad approach. We show that the interplay between Lindblad dynamics and system dynamics influences highly the spin current. For weak driving, equal rates maximize the current while strong driving shows a counter intuitive behavior. Our findings could guide to an understanding of the transport properties which are dependent on the external driving