- 2250 Elings Hall
ANDERSON MODEL OF LOCALIZATION: HAS THE FAT LADY SUNG YET?
It has been fifty-five years since Anderson proposed his model of localization (Anderson, 1958), during which the model has been examined as a function of dimension, elucidated as a model of a quantum phase transition, and more recently, generalized to consider many-body localization, among other things. However, a recent numerical study of Anderson’s original model shows that the model’s impact has not yet been fully realized. Studying the model at moderate to large disorder, we find that the nature of the insulating phase is not as uneventful and boring as has been assumed. In particular, we find that the model exhibits a “transition” from a regime of typical Anderson localized states to a regime of resonant localized states, and the two regimes are separated by what appears to be a singularity in certain measures of the electronic eigenstates, such as the inverse participation ratio. Unlike the localization-delocalization transition, this transition-like behavior is seen in all dimensions, but only for bounded disorder distributions. Our findings may explain the lack of universality seen in numerical studies of localization as a function of energy (as opposed to disorder). The resonant states evolve into the Lifschitz tail of rare fluctuation states; this suggests that the Anderson model is amenable to a much more in-depth analysis of rare fluctuation phenomena, than is possible in many-body models with quenched disorder. Our findings may also explain the lack of universality seen in numerical studies of localization as a function of energy (as opposed to disorder).