2010

Information propagation for interacting particle systems

Schuch, Norbert, Harrison, Sarah K., Osborne, Tobias J. et al.

Understand

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.

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There are two ways to obtain better bounds on the velocity. First, we can bound x y ≤ 1 2 ( λ x + y / λ ) \sqrt{xy}\leq\frac{1}{2}(\lambda x+y/\lambda) , which gives a velocity bound λ v 0 + 𝒟 τ / λ \lambda v_{0}+\mathcal{D}\tau/\lambda for any λ > 0 \lambda>0 . Second, one can solve the non-linear differential inequality ( 4
Cited in the paper.

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