Quantum mechanics

Cone (formal languages)

Theoretical physics

Algorithm

Ecology

Mathematical physics

Biology

Statistical physics

Type (biology)

Physics

Upper and lower bounds

Mathematics

Optics

Light cone

Work (physics)

Focus (optics)

Mathematical analysis

Bound state

Boson

Physical Review Letters

In this work, we investigate how quickly local perturbations propagate in interacting boson systems with Bose-Hubbard--type Hamiltonians. In general, these systems have unbounded local energies, and arbitrarily fast information propagation may occur. We focus on a specific but experimentally natural situation in which the number of bosons at any one site in the unperturbed initial state is approximately limited. We rigorously prove the existence of an almost-linear information-propagation light cone, thus establishing a Lieb-Robinson bound: the wave front grows at most as $t\text{ }{\mathrm{log}}^{2}(t)$. We prove the clustering theorem for gapped ground states and study the time complexity of classically simulating one-dimensional quench dynamics, a topic of great practical interest.

Lieb-Robinson Bound and Almost-Linear Light Cone in Interacting Boson Systems