Lieb-Robinson bounds and strongly continuous dynamics for a class of many-body fermion systems in $\mathbb{R}^d$

TL;DR

This paper establishes Lieb-Robinson bounds and proves the existence of strongly continuous dynamics for a class of UV-regularized many-body fermion systems in continuous space, advancing understanding of their temporal evolution.

Contribution

It introduces a new class of UV-regularized two-body interactions and proves Lieb-Robinson bounds and the existence of infinite-volume dynamics for these fermion systems.

Findings

Proved Lieb-Robinson estimates for fermion dynamics in $R^d$

Established propagation bounds for Schrödinger operators

Demonstrated the existence of strongly continuous automorphism groups on the CAR algebra

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.