Lieb-Robinson bounds in the continuum via localized frames

TL;DR

This paper establishes Lieb-Robinson bounds for continuum fermionic systems using localized frames, enabling analysis of quantum dynamics relevant to phenomena like the quantum Hall effect.

Contribution

It introduces the concept of lattice-localized frames in the continuum and proves Lieb-Robinson bounds for a broad class of local interactions.

Findings

Proved Lieb-Robinson bounds for continuum fermionic systems.

Established the existence of dynamics at the CAR algebra level.

Applied results to quantum Hall effect models.

Abstract

We study the dynamics of interacting fermions in the continuum. Our approach uses the concept of lattice-localized frames, which we introduce here. We first prove a Lieb-Robinson bound that is valid for a general class of local interactions, which implies the existence of the dynamics at the level of the CAR algebra. We then turn to the physical situation relevant to the (fractional) quantum Hall effect, namely the quasi-free second quantized Landau Hamiltonian to which electron-electron interactions can be added.