Multifractal wave functions in three-dimensional systems without time-reversal symmetry

Abstract

We study the multifractal properties of critical wave functions in three-dimensional systems without time-reversal symmetry. From the exact eigenstate at the mobility edge, the singularity spectrum of wave functions is obtained for two different models by a box-counting procedure. It is shown that wave functions belonging to a different universality class (orthogonal class and unitary class) have the similar singularity spectrum and generalized fractal dimension at the mobility edge in $d=3$. The value of the correlation dimension $D(2)$ which governs the anomalous diffusion of an electron is estimated to be $D(2)\ensuremath{\approx}1.5$, independent of the presence or the absence of time-reversal symmetry.