  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 wavefunction, 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.
