On Lieb-Robinson bounds for the Bose-Hubbard model

TL;DR

This paper establishes Lieb-Robinson bounds for the Bose-Hubbard model, providing insights into the speed of information and particle transport in quantum lattice systems, including cases with long-range hopping.

Contribution

It introduces Lieb-Robinson bounds for the Bose-Hubbard model on general lattices, extending previous results to include long-range hopping and initial states with almost particle-free regions.

Findings

Proves Lieb-Robinson bounds for the Bose-Hubbard model.

Derives a maximal velocity bound for particle transport.

Applicable to models with long-range hopping.

Abstract

We consider the dynamics of the Bose-Hubbard model on general lattices and prove a Lieb-Robinson bound for observables whose supports are separated by an initially almost particle-free region. We further obtain a maximal velocity bound for particle transport through an initially empty region which also applies to long-range hopping. Our techniques originate in the proofs of maximal velocity bounds for Schr\"odinger operators and scattering theory in non-relativistic QED.