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We study transport properties in boundary-driven asymmetric quantum spinchains given by $\mathit{XXZ}$ and $\mathit{XXX}$ Heisenberg models. Ourapproach exploits symmetry transformations in the Lindblad master equationassociated to the dynamics of the systems. We describe the mathematical stepsto build the unitary transformations related to the symmetry properties. Forgeneral target polarizations, we show the occurrence of the one-way streetphenomenon for the energy current, namely, the energy current does not changein magnitude and direction as we invert the baths at the boundaries. We alsoanalyze the spin current in some situations, and we prove the uniqueness of thesteady state for all investigated cases. Our results, involving nontrivialproperties of the energy flow, shall interest researchers working on thecontrol and manipulation of quantum transport.

Transport in boundary-driven quantum spin systems: One-way street for the energy current