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Spatial and Spectral Multifractality of the Local Density of States at the Mobility Edge

Bodo Huckestein·Rochus Klesse
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Abstract

We performed numerical calculations of the local density of states (LDOS) at disorder induced localization-delocalization transitions. The LDOS defines a spatial measure for fixed energy and a spectral measure for fixed position. At the mobility edge both measures are multifractal and their generalized dimensions $D(q)$ and $\tilde{D}(q)$ are found to be proportional: $D(q)=d\tilde{D}(q)$, where $d$ is the dimension of the system. This observation is consistent with the identification of the frequency-dependent length scale $L_ω\propto ω^{-1/d}$ as an effective system size. The calculations are performed for two- and three-dimensional dynamical network models with local time evolution operators. The energy dependence of the LDOS is obtained from the time evolution of the local wavefunction amplitude of a wave packet, providing a numerically efficient way to obtain information about the multifractal exponents of the system.

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Bodo Huckestein, Rochus Klesse. 1997-01-20. Spatial and Spectral Multifractality of the Local Density of States at the Mobility Edge. https://doi.org/10.1103/physrevb.55.r7303

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