Anderson localization and momentum-space entanglement

We consider Anderson localization and the associated metal-insulator transition for non-interacting fermions in D = 1, 2 space dimensions in the presence of spatially correlated on-site random potentials. To assess the nature of the wave function, we follow a recent proposal to study momentum-space entanglement. For a D = 1 model with long-range disorder correlations, both the entanglement spectrum and the entanglement entropy allow us to clearly distinguish between extended and localized states based upon a single realization of disorder. However, for other models, including the D = 2 case with long-range correlated disorder, we find that the method is not similarly successful. We analyze the reasons for its failure, concluding that the much desired generalization to higher dimensions may be problematic.