A compellingly simple proof of the speed of sound for interacting bosons

TL;DR

This paper provides a simple, rigorous proof that interacting bosonic systems on lattices have a finite speed of sound, confirming a key physical intuition about causality and information propagation in quantum many-body systems.

Contribution

It offers a remarkably straightforward proof of finite speed of sound in interacting bosonic lattice models, extending Lieb-Robinson bounds to these systems.

Findings

Finite speed of sound proven for generalized Bose-Hubbard models.

The proof is elementary and concise, making the concept more accessible.

Supports the physical expectation of causality in quantum lattice systems.

Abstract

On physical grounds, one expects locally interacting quantum many-body systems to feature a finite group velocity. This intuition is rigorously underpinned by Lieb-Robinson bounds that state that locally interacting Hamiltonians with finite-dimensional constituents on suitably regular lattices always exhibit such a finite group velocity. This also implies that causality is always respected by the dynamics of quantum lattice models. It had been a long-standing open question whether interacting bosonic systems also feature finite speeds of sound in information and particle propagation, which was only recently resolved. This work proves a strikingly simple such bound for particle propagation - shown in literally a few elementary, yet not straightforward, lines - for generalized Bose-Hubbard models defined on general lattices, proving that appropriately locally perturbed stationary states feature a finite speed of sound in particle numbers.