We will study the Falicov-Kimball model, a simple model of a strongly correlated electron system, in and out of equilibrium, using a nonequilibrium extension of the dynamical cluster approximation (DCA) and a numerically exact lattice Monte Carlo method (LMC). We use the exact LMC as a benchmark for DCA and find that the mapping to a periodized cluster introduces a substantial bias.

Using DCA we study the effect of short-range correlations on the dynamics of the model after an interaction quench. The model does not thermalize and nearest-neighbor charge correlations in the nonthermal steady state are found to be larger than in a thermal state at the same energy for quenches across the metal-insulator phase boundary. We investigate whether it is possible to describe the trapped state by a small number of parameters and find that subbands of the spectral function that correspond to DCA momentum-patches follow a roughly thermal distribution. However, the effective temperature in the energy intervals between these subbands is very hot or even negative, due to effectively different chemical potentials.

Finally, we use LMC simulations to study the spreading of charge correlations in the equilibrium model and after an interaction quench. We find that the spreading velocity reduces with interaction strength at low temperature. At higher temperature, the Fermi velocity determines the initial spreading 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.