Lieb–Robinson Bounds, Automorphic Equivalence and LPPL for Long-Range Interacting Fermions

Abstract We prove a Lieb–Robinson bound for lattice fermion models with polynomially decaying interactions, which can be used to show the locality of the quasi-local inverse Liouvillian. This allows us to prove automorphic equivalence and the local perturbations perturb locally (LPPL) principle for these systems. The proof of the Lieb–Robinson bound is based on the work of Else et al. [5], and our results also apply to spin systems. We explain why some newer Lieb–Robinson bounds for long-range spin systems cannot be used to prove the locality of the quasi-local inverse Liouvillian, and in some cases may not even hold for fermionic systems.