  We study dynamical properties of the one- and two-dimensional Falicov-Kimball
model using lattice Monte Carlo simulations. In particular, we calculate the
spreading of charge correlations in the equilibrium model and after an
interaction quench. The results show a reduction of the light-cone velocity
with interaction strength at low temperature, while the phase velocity
increases. At higher temperature, the initial spreading is determined by the
Fermi velocity of the noninteracting system and the maximum range of the
correlations decreases with increasing interaction strength. Charge order
correlations in the disorder potential enhance the range of the correlations.
We also use the numerically exact lattice Monte Carlo results to benchmark the
accuracy of equilibrium and nonequilibrium dynamical cluster approximation
calculations. It is shown that the bias introduced by the mapping to a
periodized cluster is substantial, and that from a numerical point of view, it
is more efficient to simulate the lattice model directly.
