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

A Lieb-Robinson bound for quantum spin chains with strong on-site impurities