Wave function statistics at the symplectic 2D Anderson transition: bulk properties

Abstract

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 (${\alpha }_0=2.172\pm 0.002,{\tau }_2=1.642\pm 0.004$), we report three qualitative results: (i) the anomalous dimensions are invariant under $q\to (1-q)$ 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.

4 pages, 3 figures

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