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

A. Mildenberger·F. Evers
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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 ($α_0{=}2.172\pm 0.002, τ_2{=}1.642\pm 0.004$), 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.

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A. Mildenberger, F. Evers. 2007-01-08. Wave function statistics at the symplectic 2D Anderson transition: bulk properties. https://doi.org/10.1103/physrevb.75.041303

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