  We consider a quantum spin chain with nearest neighbor interactions and
sparsely distributed on-site impurities. We prove commutator bounds for its
Heisenberg dynamics which incorporate the coupling strengths of the impurities.
The impurities are assumed to satisfy a minimum spacing, and each impurity has
a non-degenerate spectrum. Our results are proven in a broadly applicable
setting, both in finite volume and in thermodynamic limit. We apply our results
to improve Lieb-Robinson bounds for the Heisenberg spin chain with a random,
sparse transverse field drawn from a heavy-tailed distribution.
