Non-perturbative dynamics of correlated disordered flat-band system

We develop a numerical method for the time evolution of Gaussian wave packet on a flat-band-lattice in the presence of correlated disorder. We apply this to the one-dimension cross-stitch model and compare with the analytical results based on the linear band approximation. Reasonable agreement is found for the decay and dephasing process when the flat-band intersects with the dispersive band. Then we apply this method to investigate a two dimensional topological flat-band model and find quite different wave packet dynamics for different Berry phases.