Information propagation for interacting particle systems

We show that excitations of interacting quantum particles in lattice models – and thus information in these systems – 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 typically expect a bounded speed of information propagation. It 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. [The technical version, which also includes references, has been submitted as an attachment.] How fast can information propagate through a system of interacting particles? The obvious answer seems: No faster than the speed of light. While certainly correct, this is not the answer one is usually looking for. For instance, in a classical solid, liquid, or gas, perturbations rather propagate at the speed of sound, which is determined by the way the particles in the system locally interact with each other, without any reference to relativistic effects. We would like to understand whether a similar “speed of sound” exists for interacting quantum systems, limiting the propagation speed of localized excitations, i.e., (quasi-)particles. For interacting quantum spin systems, such a maximal velocity, known as the Lieb-Robinson bound, has indeed been shown. While it seems appealing that there should always be such a bound, systems of interacting bosons can show counterintuitive effects, in particular since the interpretation of excitations in terms of particles is no longer fully justified; in fact, an example of a non-relativistic system where bosons are steadily accelerated through a lattice has recently been constructed. This example suggests