Integer Quantum Hall Effect versus Anderson Transition: Numerical Comparison for Eigensolutions Statistics

Two types of the disorder-induced localization transitions, the plateau-to-plateaux transition in the Integer Quantum Hall Effect and the conventional Anderson transition in 3 dimensions are considered by using a comparative analysis. Similarities and differences of critical behavior of the eigenfunctions and eigenvalues statistics for both cases are numerically investigated within the frames of the common self-contained diagonalization technique. Both transitions reveal a number of the same universal features at criticality, including the one-parameter scaling, symmetry dependence of the eigenfucntions distributions, multifractality spectra, non-trivial branching numbers etc. Our results provide a strong support for the quantum-field theoretical description treating the two transitions as a generalized transition, i.e. a unique critical phenomenon.