scholarly journals Scattering and transport statistics at the metal-insulator transition: A numerical study of the power-law banded random-matrix model

2010 ◽  
Vol 82 (12) ◽  
Author(s):  
J. A. Méndez-Bermúdez ◽  
Victor A. Gopar ◽  
Imre Varga
Keyword(s):  
Power Law ◽  
Matrix Model ◽  
Random Matrix ◽  
Numerical Study ◽  
Insulator Transition ◽  
Metal Insulator Transition ◽  
Metal Insulator ◽  
Random Matrix Model

Conductance statistics for the power-law banded random matrix model

2010 ◽  
Author(s):  
A. J. Martínez-Mendoza ◽  
J. A. Méndez-Bermúdez ◽  
Imre Varga ◽  
Moises Martinez-Mares ◽  
Jose A. Moreno-Razo
Keyword(s):  
Power Law ◽  
Matrix Model ◽  
Random Matrix ◽  
Random Matrix Model

scholarly journals LOCAL PSEUDOGAPS AND FREE MAGNETIC MOMENTS AT THE ANDERSON METAL-INSULATOR TRANSITION: NUMERICAL SIMULATION USING POWER-LAW BAND RANDOM MATRICES

2012 ◽  
Vol 11 ◽  
pp. 102-107
Author(s):  
IMRE VARGA ◽  
STEFAN KETTEMANN ◽  
EDUARDO R. MUCCIOLO
Keyword(s):  
Power Law ◽  
Local Density ◽  
Magnetic Moments ◽  
Insulator Transition ◽  
Local Density Of States ◽  
Metal Insulator Transition ◽  
Metal Insulator ◽  
Anderson Transition ◽  
Continuous Parameter ◽  
Unitary Ensemble

At the Anderson metal-insulator transition the eigenstates develop multifractal fluctuations. Therefore their properties are intermediate between being extended and localized. As a result these wave functions are power-law correlated, which causes a substantial suppression of the local density of states at some random positions, resembling random local pseudogaps at the Fermi energy. Consequently the Kondo screening of magnetic moments is suppressed when a magnetic impurity happens to be at such a position. Due to these unscreened magnetic moments the critical exponents and multifractal dimensions at the metal-insulator transition take their smaller, unitary ensemble values for exchange couplings not exceeding a certain critical value J* ≈ .3D, where D is the band width. Here we present numerical calculations of the distribution of Kondo temperatures for the critical Power-law Band Random Matrix (PBRM) ensemble, whose properties are similar to that of the Anderson transition with the advantage of using a continuous parameter for tuning the generalized multifractal dimensions of the eigenstates.

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