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

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