Multifractal analysis of the metal-insulator transition in the 3D Anderson model I: Symmetry relation under typical averaging

Abstract

The multifractality of the critical eigenstate at the metal to insulator transition (MIT) in the three-dimensional Anderson model of localization is characterized by its associated singularity spectrum f(alpha). Recent works in 1D and 2D critical systems have suggested an exact symmetry relation in f(alpha). Here we show the validity of the symmetry at the Anderson MIT with high numerical accuracy and for very large system sizes. We discuss the necessary statistical analysis that supports this conclusion. We have obtained the f(alpha) from the box- and system-size scaling of the typical average of the generalized inverse participation ratios. We show that the best symmetry in f(alpha) for typical averaging is achieved by system-size scaling, following a strategy that emphasizes using larger system sizes even if this necessitates fewer disorder realizations.

10 pages, 12 figures

References in corpus (8)

• Exact relations between multifractal exponents at the Anderson transition
• Multifractality at the quantum Hall transition: Beyond the parabolic paradigm
• 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
• Multifractality and Conformal Invariance at 2D Metal-Insulator Transition in the Spin-Orbit Symmetry Class
• Wave function statistics at the symplectic 2D Anderson transition: bulk properties
• Critical parameters for the disorder-induced metal-insulator transition in FCC and BCC lattices
• Corner Multifractality for Reflex Angles and Conformal Invariance at 2D Anderson Metal-Insulator Transition with Spin-Orbit Scattering

Cited by in corpus (37)

• Critical parameters from generalised multifractal analysis at the Anderson transition
• Multifractal analysis with the probability density function at the three-dimensional Anderson transition
• Critical properties of the Anderson localization transition and the high dimensional limit
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model II: Symmetry relation under ensemble averaging
• Multifractal wave functions of simple quantum maps
• Statistics of renormalized on-site energies and renormalized hoppings for Anderson localization models in dimensions d=2 and d=3
• Large deviations of the Lyapunov exponent in 2D matrix Langevin dynamics with applications to one-dimensional Anderson Localization models
• Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class
• Critical states and anomalous mobility edges in two-dimensional diagonal quasicrystals
• Anderson localization transition with long-ranged hoppings : analysis of the strong multifractality regime in terms of weighted Levy sums
• Entanglement dynamics in the three-dimensional Anderson model
• Dynamic scaling relation in quantum many-body systems
• Localization-delocalization transition for disordered cubic harmonic lattices
• Wave Functions, Quantum Diffusion, and Scaling Exponents in Golden-Mean Quasiperiodic Tilings
• Statistics of the two-point transmission at Anderson localization transitions
• A critical Dyson hierarchical model for the Anderson localization transition
• Super-Universality in Anderson Localization
• Scaling of von Neumann entropy at the Anderson transition
• Quantum percolation transition in 3d: density of states, finite size scaling and multifractality
• Optimisation of multifractal analysis using box-size scaling
• Optical rogue waves in multifractal photonic arrays
• Multifractality of ab initio wave functions in doped semiconductors
• Inhomogeneous mean-field approach to collective excitations in disordered interacting bosons
• Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization
• Conformal Invariance and Multifractality at Anderson Transitions in Arbitrary Dimensions
• Multifractality and the distribution of the Kondo temperature at the Anderson transition
• Random cascade models of multifractality : real-space renormalization and travelling-waves
• Multi-fractality of the entanglement Hamiltonian eigen-modes
• Quantum multifractality as a probe of phase space in the Dicke model
• Localization, transport and edge states in a two-strand ladder network in an aperiodically staggered magnetic field
• Ring-localized states, radial aperiodicity and quantum butterflies on a Cayley tree
• Low-Dimensional Life of Critical Anderson Electron
• Multifractality in monitored single-particle dynamics
• Wavefunction extreme value statistics in Anderson localization
• Topological Dimensions from Disorder and Quantum Mechanics?
• 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
• Supercorrelated decay in a quasiperiodic nonlinear waveguide: From Markovian to non-Markovian transitions