Lieb-Robinson bound and almost-linear light-cone in interacting boson systems

TL;DR

This paper establishes an almost-linear Lieb-Robinson bound for interacting boson systems with bounded local occupation, showing that information propagates at most as t log^2(t), which has implications for quantum dynamics and simulation.

Contribution

The work rigorously proves an almost-linear light-cone in boson systems with unbounded energies under certain initial conditions, extending Lieb-Robinson bounds to these systems.

Findings

Wave-front grows at most as t log^2(t)

Clustering theorem for gapped ground states

Analysis of classical simulation complexity for 1D quench dynamics

Abstract

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 $t\log^2 (t)$. 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.