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

被引：71

作者：

Fyodorov, Yan V. ^{[1
]}

Ossipov, Alexander ^{[1
]}

Rodriguez, Alberto ^{[2
,3
]}

机构：

[1] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England

[2] Univ Warwick, Dept Phys, Coventry CV4 7AL, W Midlands, England

[3] Univ Warwick, Ctr Comp Sci, Coventry CV4 7AL, W Midlands, England

来源：

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT | 2009年

基金：

英国工程与自然科学研究理事会;

关键词：

disordered systems (theory); critical exponents and amplitudes (theory); random matrix theory and extensions; DIMENSIONAL ISING FERROMAGNET; DIAGONAL RANDOM MATRICES; BETHE LATTICE; MODEL; SYMMETRY; EXISTENCE; PHYSICS;

D O I：

10.1088/1742-5468/2009/12/L12001

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

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 an 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.

引用

页数：9

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