Giant rectification in segmented, strongly interacting spin chains despite the presence of perturbations

In Phys. Rev. Lett. 120, 200603 (2018), a segmented XXZ spin chain with zero anisotropy in one half and large on the other gave rise to current rectification which is perfect thermodynamic limit. Here we extend previous study chains interacting integrable as well non-integrable halves, considering even cases no ballistic transport can emerge either half. We demonstrate that, also this more general case, it possible obtain giant when two are sufficiently different. show that mechanism causing effect emergence of an energy gap excitation spectrum out-of-equilibrium insulating steady state biases. Finally limit there each interacting.