Wave function statistics at the symplectic two-dimensional Anderson transition: Bulk properties

The wave function statistics at the Anderson transition in a two-dimensional disordered electron gas with spin-orbit coupling is studied numerically. In addition to highly accurate exponents (alpha(0)=2.172 +/- 0.002,tau(2)=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.