Distinguishing Insulating Behavior through the Momentum Distribution function in the Anderson-Hubbard Model after an Interaction Quench

We investigate the thermalization dynamics of the Anderson-Hubbard model after an interaction quench, employing a recently developed nonequilibrium DMFT+CPA method with an iterative perturbation theory (IPT) impurity solver. While the IPT is known to be a non-conserving approximation that fails to conserve energy in the strong-coupling regime, we show that analyzing the dynamics of the momentum distribution function instead of the energy, circumvents this limitation and provides robust physical insight. We systematically compare different disorder types viz. box, binary, and Gaussian, which give rise to qualitatively different equilibrium phases, in particular, the binary disorder giving rise to a band-gap insulator apart from the Mott insulating phase. The momentum distribution function shows the presence of either a prethermalized state or an oscillating thermalization depending on whether the equilibrium state has an insulating gap. In addition, we can also distinguish between the Mott and band gaps by the emergence of a disorder (in)dependent time scale in the oscillation.