Critical parameters from generalised multifractal analysis at the Anderson transition

Abstract

We propose a generalization of multifractal analysis that is applicable to the critical regime of the Anderson localization-delocalization transition. The approach reveals that the behavior of the probability distribution of wavefunction amplitudes is sufficient to characterize the transition. In combination with finite-size scaling, this formalism permits the critical parameters to be estimated without the need for conductance or other transport measurements. Applying this method to high-precision data for wavefunction statistics obtained by exact diagonalization of the three-dimensional Anderson model, we estimate the critical exponent $\nu =1.58\pm 0.03$.

5 pages, 3 figures, 2 tables

References in corpus (26)

• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Critical Phenomena and Renormalization-Group Theory
• Experimental observation of the Anderson transition with atomic matter waves
• Corrections to scaling at the Anderson transition
• Statistics and Scaling in Disordered Mesoscopic Electron Systems
• Visualizing Critical Correlations near the Metal-Insulator Transition in Ga1-xMnxAs
• Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle
• Mutifractal Analysis of Broadly Distributed Observables at Criticality
• Exact relations between multifractal exponents at the Anderson transition
• The Quantum Hall Transition in Real Space: From Localized to Extended States
• Observation of multifractality in Anderson localization of ultrasound
• Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves: Theory and Experiment
• Asymptotics of Universal Probability of Neighboring Level Spacings at the Anderson Transition
• Multifractal analysis with the probability density function at the three-dimensional Anderson transition
• Multifractality at the quantum Hall transition: Beyond the parabolic paradigm
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model I: Symmetry relation under typical averaging
• Direct comparison between potential landscape and local density of states in a disordered two-dimensional electron system
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model II: Symmetry relation under ensemble averaging
• Boundary multifractality at the integer quantum Hall plateau transition: implications for the critical theory
• Multifractal analysis of the metal-insulator transition in anisotropic systems
• Energy-level statistics at the metal-insulator transition in anisotropic systems
• A semiclassical theory of the Anderson transition
• Critical properties of the metal-insulator transition in anisotropic systems
• Cross-correlations in scaling analyses of phase transitions
• Numerical verification of universality for the Anderson transition

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