  In order to better understand the minimal ingredients for thermal
rectification, we perform a detailed investigation of a simple spin chain,
namely, the open XX model with a Lindblad dynamics involving global
dissipators. We use a Jordan-Wigner transformation to derive a mathematical
formalism to compute the heat currents and other properties of the steady
state.
  We have rigorous results to prove the occurrence of thermal rectification
even for slightly asymmetrical chains. Interestingly, we describe cases where
the rectification does not decay to zero as we increase the system size, that
is, the rectification remains finite in the thermodynamic limit. We also
describe some numerical results for more asymmetrical chains. The presence of
thermal rectification in this simple model indicates that the phenomenon is of
general occurrence in quantum spin systems.
