The wavefunction statistics at the Anderson transition in a 2d disordered electron gas with spin-orbit coupling is studied numerically. In addition to highly accurate exponents (α0=2.172±0.002,τ2=1.642±0.004), we report three qualitative results: (i) the anomalous dimensions are invariant under q→(1−q) which is in agreement with a recent analytical prediction and supports the universality hypothesis. (ii) The multifractal spectrum is not parabolic and therefore differs from behavior suspected, e.g., for (integer) quantum Hall transitions in a fundamental way. (iii) The critical fixed point satisfies conformal invariance.
@article{arxiv.cond-mat/0608560,
title = {Wave function statistics at the symplectic 2D Anderson transition: bulk properties},
author = {A. Mildenberger and F. Evers},
journal= {arXiv preprint arXiv:cond-mat/0608560},
year = {2007}
}