Anderson localization transition and eigenfunction multifractality in ensemble of ultrametric random matrices

Details Anderson localization transition and eigenfunction multifractality in ensemble of ultrametric random matrices Anderson localization transition and eigenfunction multifractality in ensemble of ultrametric random matrices

2009-09-25

arxiv.org/abs/0909.4704v2

J. Stat. Mech. (2009) L12001

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

9 pages, 2 figures; slightly expanded version

Scientific paper

We demonstrate that by considering disordered single-particle Hamiltonians (or their random matrix versions) on ultrametric spaces one can generate an interesting class of models exhibiting Anderson metal-insulator 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.

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