Level statistics and phase diagram for the Quantum Hall effect
Abstract
We report results of numerical studies of the integer quantum Hall effect (IQHE) on a twodimensional square lattice with noninteracting electrons in the presence of disordered potential and a uniform magnetic field applied perpendicular to the lattice of size upto 4000 x 4000 sites. It is shown that shortrange spectral fluctuations exhibit critical behavior, giving the correlation length exponent ν≈ 2.36 and the irrelevant exponent y≈ 0.8. The latter is extracted by taking corrections to the scaling into account. The longrange fluctuations are described by the critical spectral compressibility i≈ 0.135, consistent with the multifractal dimension D_{2} found numerically from the distributions of momenta of the participation ratio P(I_p) at the transition between the Hall plateaus. We show that in the quasi1D geometry the localization length oscillates in the quantized limit, when the Hall conductance undergoes a crossover from ShubnikovDeHaas regime to the IQHE. It `doubles' at the GOEGUE crossover (at weak magnetic fields ωτ≪ 1). Comparison between the IQHE and the 3D Anderson transition confirms similarity for the parametric spectral statistics and the distributions of wavefunctions amplitudes. Both are used to precisely track the floatingup of currectcarring states and to compute the global phase diagram.
 Publication:

APS March Meeting Abstracts
 Pub Date:
 March 2004
 Bibcode:
 2004APS..MAR.R1265Z