On the quantum dynamics of long-ranged Bose-Hubbard Hamiltonians

TL;DR

This paper investigates the quantum dynamics of long-range Bose-Hubbard models, establishing bounds on particle propagation and developing new analytical methods to handle unbounded long-range interactions.

Contribution

It provides the first thermodynamically stable Lieb-Robinson bound for long-range Bose-Hubbard Hamiltonians and introduces the multiscale ASTLO method for such systems.

Findings

Proved ballistic propagation bounds for exponents $oldsymbol{ extit{ extalpha}>d+1}$.

Established the first thermodynamically stable Lieb-Robinson bound for these Hamiltonians.

Developed the multiscale ASTLO method for analyzing long-range quantum systems.

Abstract

We study the quantum dynamics generated by Bose-Hubbard Hamiltonians with long-ranged (power law) terms. We prove two ballistic propagation bounds for suitable initial states: (i) A bound on all moments of the local particle number for all power law exponents $\alpha>d+1$ in $d$ dimensions, the sharp condition. (ii) The first thermodynamically stable Lieb-Robinson bound (LRB) for these Hamiltonians. To handle the long-ranged and unbounded terms, we further develop the multiscale ASTLO (adiabatic space time localization observables) method introduced in our recent work [arXiv:2310.14896].