  We address a keystone problem for the progress of phononics: the proposal of
efficient thermal diodes. Aiming the disclosure of an easy itinerary for the
building of a heat rectifier, we investigate unsophisticated systems linked to
simple thermal baths, precisely, asymmetric quantum Ising models, i.e., simple
quadratic models, involving only one spin component. We analytically show the
occurrence of thermal rectification for the case of a chain with interactions
long enough to connect the first to the last site. Moreover, we describe cases
of a perfect rectification, i.e., finite heat flow in one direction, and zero
current in the opposite direction. We argue to indicate that the ingredients
for the rectification are just given by the quantum nature of the baths and
dynamics, and by the structural asymmetry of the system, here in the inter-site
interactions. We believe that the description of a perfect thermal
rectification in a simple many-body quantum model, that is, the presentation of
a simple itinerary for the building of a diode shall stimulate theoretical and
experimental research on the theme.
