On the microscopic propagation speed of long-range quantum many-body systems

TL;DR

This paper establishes the first thermodynamically stable bounds on the microscopic propagation speed in long-range quantum many-body systems, advancing understanding of particle transport at small scales.

Contribution

It introduces a novel multiscale ASTLO method to derive stable bounds on particle transport speed in long-range bosonic systems.

Findings

First bound on microscopic particle transport speed in long-range systems

Development of a multiscale ASTLO method

Potential for thermodynamically stable Lieb-Robinson bounds

Abstract

We consider the time-dependent Schr\"odinger equation that is generated on the bosonic Fock space by a long-range quantum many-body Hamiltonian. We derive the first bound on the maximal speed of particle transport in these systems that is thermodynamically stable and holds all the way down to microscopic length scales. For this, we develop a novel multiscale rendition of the ASTLO (adiabatic spacetime localization observables) method. Our result opens the door to deriving the first thermodynamically stable Lieb-Robinson bounds on general local operators for these long-range interacting bosonic systems.