Anomalous transport in the Aubry-Andre-Harper model in isolated and open systems

We study the high-temperature transport behavior of the Aubry-Andre-Harper (AAH) model, both in an isolated thermodynamic limit and in an open system. At the critical point of the AAH model, we find hints of superdiffusive behavior from the scaling of spread of an initially localized wave packet. On the other hand, when connected to two baths with different chemical potentials at the two ends, we find that the critical point shows clear subdiffusive scaling of current with system size. We provide an explanation for this by showing that the current scaling with system size is entirely governed by the behavior of the single-particle eigenfunctions at the boundary sites where the baths are attached. We also look at the particle density profile in the nonequilibrium steady state of the open system when the two baths are at different chemical potentials. We find that the particle density profile has distinctly different behavior in the delocalized, critical, and localized phases of the AAH model.