Establishing non-zero energy currents with the one-way street phenomenon and other symmetry properties in boundary driven spin systems

The aim of this paper is the investigation of properties of the energy current of usual (frequently found in the literature) boundary driven spin systems. For inhomogeneous Heisenberg (XXZ and XXX) spin chains, we numerically compute the steady state, in the absence of an external magnetic field, and confirm the previously shown occurrence of the one-way street phenomenon, precisely, there is a nonzero energy current that preserves its magnitude and direction as we invert the baths at the edges, an effect stronger than the perfect rectification (which means current in a direction and zero current as we invert the baths). The consideration of several different polarizations at the edges reestablishes that it is a ubiquitous phenomenon. And, even for these inhomogeneous versions of spin chains, we also establish, by analytical methods, other symmetry properties of the energy current and confirm them by numerical computations.