Lieb–Robinson Bounds and Strongly Continuous Dynamics for a Class of Many-Body Fermion Systems in $${\mathbb {R}}^d$$

Abstract

We introduce a class of UV-regularized two-body interactions for fermions in $\mathbb{R}^d$ and prove a Lieb-Robinson estimate for the dynamics of this class of many-body systems. As a step toward this result, we also prove a propagation bound of Lieb-Robinson type for Schr\"odinger operators. We apply the propagation bound to prove the existence of infinite-volume dynamics as a strongly continuous group of automorphisms on the CAR algebra.