Monday, March 11, 2013

1303.2012 (F. L. Metz et al.)

Transition between localized and extended states in the hierarchical
Anderson model

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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