Information propagation for interacting particle systems

TL;DR

This paper proves that excitations in interacting quantum lattice systems propagate at a finite speed, extending the concept of Lieb-Robinson bounds to a broad class of models including spins, bosons, fermions, anyons, and quantum fields.

Contribution

It provides a simple, general argument demonstrating finite speed of information propagation across various quantum many-body systems and dynamics.

Findings

Finite speed of sound in quantum lattice models

Applicable to spins, bosons, fermions, anyons, and mixtures

Extends to dissipative and continuum quantum field dynamics

Abstract

We show that excitations of interacting quantum particles in lattice models always propagate with a finite speed of sound. Our argument is simple yet general and shows that by focusing on the physically relevant observables one can generally expect a bounded speed of information propagation. The argument applies equally to quantum spins, bosons such as in the Bose-Hubbard model, fermions, anyons, and general mixtures thereof, on arbitrary lattices of any dimension. It also pertains to dissipative dynamics on the lattice, and generalizes to the continuum for quantum fields. Our result can be seen as a meaningful analogue of the Lieb-Robinson bound for strongly correlated models.