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

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.

Automated summary

This study considers a quantum spin chain with nearest neighbor interactions and sparsely distributed on-site impurities. Commutator bounds for its Heisenberg dynamics, which incorporate the coupling strengths of the impurities, are proven. The results apply to both finite volume and thermodynamic limit scenarios, and can be used to improve Lieb-Robinson bounds for the Heisenberg spin chain with a random, sparse transverse field drawn from a heavy-tailed distribution.