3 research outputs found
Multifractality beyond the Parabolic Approximation: Deviations from the Log-normal Distribution at Criticality in Quantum Hall Systems
Based on differences of generalized R\'enyi entropies nontrivial constraints
on the shape of the distribution function of broadly distributed observables
are derived introducing a new parameter in order to quantify the deviation from
lognormality. As a test example the properties of the two--measure random
Cantor set are calculated exactly and finally using the results of numerical
simulations the distribution of the eigenvector components calculated in the
critical region of the lowest Landau--band is analyzed.Comment: LaTeX 4 pages, 3 EPS included, to appear in Europhysics Letter
Correlation of eigenstates in the critical regime of quantum Hall systems
We extend the multifractal analysis of the statistics of critical wave
functions in quantum Hall systems by calculating numerically the correlations
of local amplitudes corresponding to eigenstates at two different energies. Our
results confirm multifractal scaling relations which are different from those
occurring in conventional critical phenomena. The critical exponent
corresponding to the typical amplitude, , gives an almost
complete characterization of the critical behavior of eigenstates, including
correlations. Our results support the interpretation of the local density of
states being an order parameter of the Anderson transition.Comment: 17 pages, 9 Postscript figure