Maximal speed for macroscopic particle transport in the Bose-Hubbard model

TL;DR

This paper establishes a rigorous ballistic upper bound on macroscopic particle transport in the Bose-Hubbard model, extending Lieb-Robinson type bounds to bosonic systems with broad initial states.

Contribution

It provides the first general ballistic upper bound for particle transport in the Bose-Hubbard model, covering a wide class of initial states including Mott states.

Findings

First rigorous bound for bosonic lattice gases.

Applicable to various lattice geometries with limited long-range hopping.

Resolves a longstanding open problem in quantum many-body dynamics.

Abstract

The Lieb-Robinson bound asserts the existence of a maximal propagation speed for the quantum dynamics of lattice spin systems. Such general bounds are not available for most bosonic lattice gases due to their unbounded local interactions. Here we establish for the first time a general ballistic upper bound on macroscopic particle transport in the paradigmatic Bose-Hubbard model. The bound is the first to cover a broad class of initial states with positive density including Mott states, which resolves a longstanding open problem. It applies to Bose-Hubbard type models on any lattice with not too long-ranged hopping. The proof is rigorous and rests on controlling the time evolution of a new kind of adiabatic spacetime localization observable via iterative differential inequalities.