Phase-space visualization of a metal–insulator transition

The Aubry–André model with its transition from a delocalized to a localized phase in one dimension is particularly well suited for a phase-space study of such a metal–insulator transition. The dependence of the Husimi function on the potential strength is discussed and described quantitatively by means of marginal distributions and the inverse participation ratio in phase space. The phase-space representation not only helps to visualize the metal–insulator transition but also sheds light on the question why such a transition is possible in a one-dimensional system. Differences and similarities between the Aubry–André model and the Anderson model in one and higher dimensions, respectively, will be pointed out.