Rectification and one-way street for the energy current in boundary-driven asymmetric quantum spin chains

Motivated by the demand for efficient quantum devices to engineer energy transport, we analyze some inhomogeneous quantum spin systems, including XXZ chains, with magnetization baths at the ends. With a goal of finding general properties, we study the effects of suitable transformations on the boundary-driven Lindblad master equation associated with the dynamics of the systems. For asymmetric models with target polarization at the edges or twisted XY boundary gradients, we show the properties of the steady state, which establish the features of the energy current irrespective of the system size and the regime of transport. We show the ubiquitous occurrence of energy rectification and, more interestingly, of an unusual phenomenon: in the absence of an external magnetic field, there is a one-way street for the energy current, i.e., the direction of the energy current does not change as we invert the magnetization baths at the boundaries. Given the extensiveness of the procedures, which essentially involve the properties of the Lindblad master equation, our results certainly follow for other interactions and other boundary conditions. Moreover, our results indicate graded spin chains as genuine quantum rectifiers.