Information propagation for interacting-particle systems

We study the speed at which information propagates through systems of interacting quantum particles moving on a regular lattice and show that for a certain class of initial conditions there exists a maximum speed of sound at which information can propagate. Our 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 an analog of the Lieb-Robinson bound for strongly correlated models.

Figure 1

Schematic representation of the “light cone” of particles initially placed into a region $R$ of a lattice (large yellow circles) and then propagating in time $t$ in a way governed by an interacting quantum model, outside of which the influence of these particles is exponentially suppressed.