F. L. Metz, L. Leuzzi, G. Parisi, V. Sacksteder IV
We present strong numerical evidence for the existence of a localization-delocalization transition in the eigenstates of the 1-D Anderson model with long-range hierarchical hopping. We find a finite critical disorder strength Wc where the average inverse participation ratio goes to zero; at small disorder W < Wc the model lies in a delocalized phase. This result is based on numerical calculation of the inverse participation ratio in the infinite volume limit using a renormalization group approach facilitated by the model's hierarchical structure. Our finding should stimulate interest in the hierarchical Anderson model as a simplified and tractable model of the Anderson localization transition which occurs in finite-dimensional systems with short-range hopping.
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http://arxiv.org/abs/1303.2012
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