  We study quantum transport properties of an open Heisenberg XXZ spin 1/2
chain driven by a pair of Lindblad jump operators satisfying a global
`microcanonical' constraint, i.e. conserving the total magnetization. We will
show that this system has an additional discrete symmetry which is particular
to the Liouvillean description of the problem. Such symmetry reduces the
dynamics even more than what would be expected in the standard Hilbert space
formalism and establishes existence of multiple steady states. Interestingly,
numerical simulations of the XXZ model suggest that a pair of distinct
non-equilibrium steady states becomes indistinguishable in the thermodynamic
limit, and exhibit sub-diffusive spin transport in the easy-axis regime of
anisotropy Delta > 1.
