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We give an exact matrix product steady state and matrix product forms oflocal observables for the bulk impurity-doped XXZ spin model coupled todissipators at both ends, whose dynamics is described by the Lindblad quantummaster equation. We find that local magnetization is induced at the impuritysite when the spin current flows, which is contrary to the usual situationwhere current suppresses magnetization due to heating. It is proved that thiscurrent-induced magnetization survives in the thermodynamic limit, and the spincurrent does not depend on the impurity strength. We discuss the role of bulkintegrability by comparing the results with those of non-integrable modelssolved numerically by the quantum trajectory method.

Exact steady states of the impurity-doped XXZ spin chain coupled to dissipators