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 Schrödinger 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.

arXiv commentCorrected equation (1.5) in the introduction

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• Maximal speed for macroscopic particle transport in the Bose-Hubbard model
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• Maximal Speed of Quantum Propagation
• On Lieb-Robinson bounds for a class of continuum fermions
• Locality bounds for quantum dynamics at low energy
• On the thermodynamic limit of interacting fermions in the continuum