Distribution of fractal dimensions at the Anderson transition

Abstract

We investigated numerically the distribution of participation numbers in the 3d Anderson tight-binding model at the localization-delocalization threshold. These numbers in {\em one} disordered system experience strong level-to-level fluctuations in a wide energy range. The fluctuations grow substantially with increasing size of the system. We argue that the fluctuations of the correlation dimension, $D_2$ of the wave functions are the main reason for this. The distribution of these correlation dimensions at the transition is calculated. In the thermodynamic limit ($L\to \infty$) it does not depend on the system size $L$. An interesting feature of this limiting distribution is that it vanishes exactly at $D_{2max}=1.83$, the highest possible value of the correlation dimension at the Anderson threshold in this model.

Cited by in corpus (22)

• Fluctuations of the inverse participation ratio at the Anderson transition
• Multifractality and critical fluctuations at the Anderson transition
• Eigenfunction fractality and pseudogap state near superconductor-insulator transition
• Statistics of Resonances and Delay Times in Random Media: Beyond Random Matrix Theory
• Dimensionality dependence of the wave function statistics at the Anderson transition
• Fluctuations of the correlation dimension at metal-insulator transitions
• Critical Hamiltonians with long range hopping
• Critical statistics in a power-law random banded matrix ensemble
• Fluctuation of the Correlation Dimension and the Inverse Participation Number at the Anderson Transition
• Probing the eigenfunction fractality with a stop watch
• Wave function statistics at the symplectic 2D Anderson transition: bulk properties
• Replacing energy by von Neumann entropy in quantum phase transitions
• Resonance width distribution for high-dimensional random media
• Localization and Superconductivity in Doped Semiconductors
• Anomalously localized states and multifractal correlations of critical wavefunctions in two-dimensional electron systems with spin-orbital interactions
• Correlated random band matrices: localization-delocalization transitions
• Reentrant topological phases and spin density wave induced by 1D moiré potentials
• Critical States Embedded in the Continuum
• Emergent fractals in dirty topological crystals
• Determination of the Electronic Localized-to-Extended-State Transition Point around the Metal-to-Insulator Transition Region of Fluid Mercury Using the Framework of Multifractal Analysis
• Understanding the approach to thermalization from the eigenspectrum of non-Abelian gauge theories
• Holographic nature of critical quantum states of proteins