  We study the rectification of heat current in an XXZ chain segmented in two
parts. We model the effect of the environment with Lindblad heat baths. We show
that, in our system, rectification is large for strong interactions in half of
the chain and if one bath is at cold enough temperature. For the numerically
accessible chain lengths, we observe that the rectification increases with the
system size. We gain insight in the rectification mechanism by studying
two-time correlations in the steady state. The presence of interactions also
induces a strong nonlinear response to the temperature difference, resulting in
superlinear and negative differential conductance regimes.
