  Using Lindblad dynamics we study quantum spin systems with dissipative
boundary dynamics that generate a stationary nonequilibrium state with a
non-vanishing spin current that is locally conserved except at the boundaries.
We demonstrate that with suitably chosen boundary target states one can solve
the many-body Lindblad equation exactly in any dimension. As solution we obtain
pure states at any finite value of the dissipation strength and any system
size. They are characterized by a helical stationary magnetization profile and
a superdiffusive ballistic current of order one, independent of system size
even when the quantum spin system is not integrable. These results are derived
in explicit form for the one-dimensional spin-1/2 Heisenberg chain and its
higher-spin generalizations (which include for spin-1 the integrable
Zamolodchikov-Fateev model and the bi-quadratic Heisenberg chain). The
extension of the results to higher dimensions is straightforward.
