We study heat transport in quantum spin systems analytically and numerically. First, we demonstrate that heat current through a two-level quantum spin system can be modulated from zero to a finite value by tuning a magnetic field. Second, we show tha
t a spin system, consisting of two dissimilar parts - one is gapped and the other is gapless, exhibits current rectification and negative differential thermal resistance. Possible experimental realizations by using molecular junctions or magnetic materials are discussed.
