Lieb-Robinson bounds, automorphic equivalence and LPPL for long-range interacting fermions

TL;DR

This paper establishes Lieb-Robinson bounds for long-range interacting fermions, enabling proofs of automorphic equivalence and LPPL, and discusses limitations of existing bounds for such systems.

Contribution

It introduces a Lieb-Robinson bound for polynomially decaying fermionic interactions, extending locality results to these models and spin systems.

Findings

Proved Lieb-Robinson bounds for long-range fermionic systems.

Demonstrated automorphic equivalence and LPPL for these models.

Highlighted limitations of existing bounds for fermionic systems.

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. (2020), 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.