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 $({\ensuremath{\alpha}}_{0}=2.172\ifmmode\pm\else\textpm\fi{}0.002,{\ensuremath{\tau}}_{2}=1.642\ifmmode\pm\else\textpm\fi{}0.004)$, we report three qualitative results. (i) The anomalous dimensions are invariant under $q\ensuremath{\rightarrow}(1\ensuremath{-}q)$ 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.