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We find novel site-dependent Lax operators in terms of which we demonstrateexact solvability of a dissipatively driven XYZ spin-1/2 chain in the Zenolimit of strong dissipation, with jump operators polarizing the boundary spinsin arbitrary directions. We write the corresponding nonequilibrium steady stateusing an inhomogeneous MPA, where the constituent matrices satisfy a simple setof linear recurrence relations. Although these matrices can be embedded into aninfinite-dimensional auxiliary space, we have verified that they cannot besimultaneously put into a tridiagonal form, not even in the case of axiallysymmetric (XXZ) bulk interactions and general nonlongitudinal boundarydissipation. We expect our results to have further fundamental applications forthe construction of nonlocal integrals of motion for the open XYZ model witharbitrary boundary fields, or the eight-vertex model.

Inhomogeneous MPA and exact steady states of boundary driven spin chains at large dissipation