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 two-dimensional square lattice with non-interacting 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 short-range 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 long-range fluctuations are described by the critical spectral compressibility i≈ 0.135, consistent with the multifractal dimension D2 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 quasi-1D geometry the localization length oscillates in the quantized limit, when the Hall conductance undergoes a crossover from Shubnikov-DeHaas regime to the IQHE. It `doubles' at the GOE-GUE 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 floating-up of currect-carring states and to compute the global phase diagram.
- Publication:
-
APS March Meeting Abstracts
- Pub Date:
- March 2004
- Bibcode:
- 2004APS..MAR.R1265Z