We consider generic interacting chain of qubits, which are coupled at the
edges to baths of fixed polarizations. We can determine the nonequilibrium
steady states, described by the fixed point of the Lindblad Master Equation.
Under rather general assumptions about local pumping and interactions,
symmetries of the reduced density matrix are revealed. The symmetries
drastically restrict the form of the steady density matrices in such a way that
an exponentially large subset of one--point and many--point correlation
functions are found to vanish. As an example we show how in a Heisenberg spin
chain a suitable choice of the baths can completely switch off either the spin
or the energy current, or both of them, despite the presence of large boundary
gradients.Comment: 8 pages, 3 Figure
