LETTER: The Anderson localization transition and eigenfunction multifractality in an ensemble of ultrametric random matrices
Abstract
We demonstrate that by considering disordered singleparticle Hamiltonians (or their random matrix versions) on ultrametric spaces one can generate an interesting class of models exhibiting an Anderson metalinsulator transition. We use the weak disorder virial expansion to determine the critical value of the parameters and to calculate the values of the multifractal exponents for inverse participation ratios. Direct numerical simulations agree favourably with the analytical predictions.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 December 2009
 DOI:
 10.1088/17425468/2009/12/L12001
 arXiv:
 arXiv:0909.4704
 Bibcode:
 2009JSMTE..12L.001F
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 9 pages, 2 figures