Mutifractal Analysis of Broadly Distributed Observables at Criticality

Abstract

The multifractal analysis of disorder induced localization-delocalization transitions is reviewed. Scaling properties of this transition are generic for multi parameter coherent systems which show broadly distributed observables at criticality. The multifractal analysis of local measures is extended to more general observables including scaling variables such as the conductance in the localization problem. The relation of multifractal dimensions to critical exponents such as the order parameter exponent $\beta$ and the correlation length exponent $\nu$ is investigated. We discuss a number of scaling relations between spectra of critical exponents, showing that all of the critical exponents necessary to characterize the critical phenomenon can be obtained within the generalized multifractal analysis. Furthermore we show how bounds for the correlation length exponent $\nu$ are obtained by the typical order parameter exponent ${\alpha }_0$ and make contact between the multifractal analysis and the finite size scaling approach in 2-d by relying on conformal mapping arguments.

39 pages, LateX, THP-J-94-1

Cited by in corpus (135)

• Anderson Transitions
• Scaling Theory of the Integer Quantum Hall Effect
• Statistics and Scaling in Disordered Mesoscopic Electron Systems
• Fluctuations of the inverse participation ratio at the Anderson transition
• Multifractality and critical fluctuations at the Anderson transition
• Multifractal finite-size-scaling and universality at the Anderson transition
• Two-dimensional conformal field theory for disordered systems at criticality
• Critical parameters from generalised multifractal analysis at the Anderson transition
• Universal behavior beyond multifractality in quantum many-body systems
• Exact calculation of multifractal exponents of the critical wave function of Dirac fermions in a random magnetic field
• Investigation of quantum transport by means of O(N) real-space methods
• Spatially heterogeneous ages in glassy dynamics
• Multifractality of wavefunctions at the quantum Hall transition revisited
• Multifractal analysis with the probability density function at the three-dimensional Anderson transition
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model I: Symmetry relation under typical averaging
• Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors
• Critical properties of the Anderson localization transition and the high dimensional limit
• Finite Size Effects and Irrelevant Corrections to Scaling near the Integer Quantum Hall Transition
• Dimensionality dependence of the wave function statistics at the Anderson transition
• Point-Contact Conductances at the Quantum Hall Transition
• Conformal invariance, multifractality, and finite-size scaling at Anderson localization transitions in two dimensions
• Universal Multifractality in Quantum Hall Systems with Long-Range Disorder Potential
• Critical eigenstates and their properties in one and two dimensional quasicrystals
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model II: Symmetry relation under ensemble averaging
• Many-body Multifractality throughout Bosonic Superfluid and Mott Insulator Phases
• Critical phase dualities in 1D exactly-solvable quasiperiodic models
• Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model
• Dimensional dependence of the metal-insulator transition
• Interactions, Localization, and the Integer Quantum Hall Effect
• Fluctuation of the Correlation Dimension and the Inverse Participation Number at the Anderson Transition
• Critical properties of the Anderson transition in random graphs: two-parameter scaling theory, Kosterlitz-Thouless type flow and many-body localization
• Spectral Compressibility at the Metal-Insulator Transition of the Quantum Hall Effect
• Critical regime of two dimensional Ando model: relation between critical conductance and fractal dimension of electronic eigenstates
• Boundary criticality at the Anderson transition between a metal and a quantum spin Hall insulator in two dimensions
• Network Model for a 2D Disordered Electron System with Spin-Orbit Scattering
• Copolymer Networks and Stars: Scaling Exponents
• Monitoring the localization-delocalization transition within a 1D model with non-random long-range interaction
• Non-Hermitian Aubry-André model with Power-Law Hopping
• Termination of Multifractal Behaviour for Critical Disordered Dirac Fermions
• $f(\alpha )$ Multifractal spectrum at strong and weak disorder
• Universality and multifractal behaviour of spin-spin correlation functions in disordered Potts models
• Wave function statistics at the symplectic 2D Anderson transition: bulk properties
• Boundary criticality and multifractality at the 2D spin quantum Hall transition
• Exact Multifractality for Disordered N-Flavour Dirac Fermions in Two Dimensions
• Distribution of fractal dimensions at the Anderson transition
• Kondo-Anderson Transitions
• Flat-band-based multifractality in the all-band-flat diamond chain
• Copolymer Networks: Multifractal dimension spectra in polymer field theory
• Extracting Critical Exponent by Finite-Size Scaling with Convolutional Neural Networks
• Critical Metal Phase at the Anderson Metal-Insulator Transition with Kondo Impurities
• Disorder-Induced Vibrational Localization
• Multifractal nature of the surface local density of states in three-dimensional topological insulators with magnetic and nonmagnetic disorder
• Termination of typical wavefunction multifractal spectra at the Anderson metal-insulator transition: Field theory description using the functional renormalization group
• Anomalous multifractality in quantum chains with strongly correlated disorder
• Disorder driven multifractality transition in Weyl nodal loops
• Multifractality of Hamiltonians with power-law transfer terms
• Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class
• Compressibility stripes for mesoscopic quantum Hall samples
• Semi-Poisson statistics in quantum chaos
• Localization as an entanglement phase transition in boundary-driven Anderson models
• Metal-insulator transition in two-dimensional disordered systems with power-law transfer terms
• Multifractal dimensions for critical random matrix ensembles
• Finite Cluster Typical Medium Theory for Disordered Electronic Systems
• Generalized Multiband Typical Medium Dynamical Cluster Approximation: Application to (Ga,Mn)N
• Power law hopping of single particles in one-dimensional non-Hermitian quasicrystals
• Anderson Transitions: Criticality, Symmetries, and Topologies
• Multifractality of the quantum Hall wave functions in higher Landau levels
• Many-Body Localization Transition in Random Quantum Spin Chains with Long-Range Interactions
• Critical generalized inverse participation ratio distributions
• Resolution of the exponent puzzle for the Anderson transition in doped semiconductors
• Correlation of eigenstates in the critical regime of quantum Hall systems
• Effective Cluster Typical Medium Theory for Diagonal Anderson Disorder Model in One- and Two-Dimensions
• Multifractal properties of critical eigenstates in two-dimensional systems with symplectic symmetry
• Mesoscopic fluctuations of the single-particle Green's function at Anderson transitions with Coulomb interaction
• Modeling Disordered Quantum Systems with Dynamical Networks
• Anomalously localized states and multifractal correlations of critical wavefunctions in two-dimensional electron systems with spin-orbital interactions
• Disordered Electrons in a Strong Magnetic Field: Transfer Matrix Approaches to the Statistics of the Local Density of States
• Directed polymer in a random medium of dimension 1+3 : multifractal properties at the localization/delocalization transition
• Quasiperiodicity hinders ergodic Floquet eigenstates
• Generalized multifractality at spin quantum Hall transition
• Exponential Orthogonality Catastrophe at the Anderson Metal-Insulator Transition
• On the multifractal statistics of the local order parameter at random critical points : application to wetting transitions with disorder
• Optimisation of multifractal analysis using box-size scaling
• ${\mathcal{L}}^2$ localization landscape for highly-excited states
• Spectral Properties of the Chalker-Coddington Network
• Correlated random band matrices: localization-delocalization transitions
• Multifractality beyond the Parabolic Approximation: Deviations from the Log-normal Distribution at Criticality in Quantum Hall Systems
• Short-Range Ising Spin Glass: Multifractal Properties
• On the critical weight statistics of the Random Energy Model and of the Directed Polymer on the Cayley Tree
• Multifractality of ab initio wave functions in doped semiconductors
• Breakdown of Conformal Invariance at Strongly Random Critical Points
• Long-range hopping in a quasiperiodic potential weakens the non-Hermitian skin effect
• Towards a Comprehensive Theory of Metal-Insulator Transitions in Doped Semiconductors
• Self-duality of One-dimensional Quasicrystals with Spin-Orbit Interaction
• Universality of Anderson transition in two-dimensional systems of symplectic symmetry class
• Critical level statistics and anomalously localized states at the Anderson transition
• Metal-insulator transitions in anisotropic 2d systems
• Statistics of Conductances and Subleading Corrections to Scaling near the Integer Quantum Hall Plateau Transition
• The Influence of Percolation in the generalized Chalker-Coddington Model
• Nodal vacancy bound states and resonances in three-dimensional Weyl semimetals
• Character of eigenstates of the 3D disordered Anderson Hamiltonian
• Is it possible to observe experimentally a metal-insulator transition in ultra cold atoms?
• Partitioning Schemes and Non-Integer Box Sizes for the Box-Counting Algorithm in Multifractal Analysis
• Critical properties in long-range hopping Hamiltonians
• Multi-fractality of the entanglement Hamiltonian eigen-modes
• Quantum multifractality as a probe of phase space in the Dicke model
• Random cascade models of multifractality : real-space renormalization and travelling-waves
• Hartree-Fock study of an Anderson metal-insulator transition in the presence of Coulomb interaction: Two types of mobility edges and their multifractal scaling exponents
• On the multifractal dimensions and statistical properties of critical ensembles characterized by the three classical Wigner-Dyson symmetry classes
• On the localization transition in three dimensions: Monte-Carlo simulation of a non-linear $\sigma$-model
• Nonergodic thermodynamics of disordered ferromagnets and ferroelectrics
• Correlation Exponent and Anomalously Localized States at the Critical Point of the Anderson Transition
• Multiscaling Anderson localization of cosmic electromagnetic fields
• Ring-localized states, radial aperiodicity and quantum butterflies on a Cayley tree
• Scattering and transport properties of the three classical Wigner-Dyson ensembles at the Anderson transition
• Wave functions in the Critical Phase: a Planar \textit{Sierpiński} Fractal Lattice
• Mesoscopic fluctuations of the local density of states in interacting electron systems
• Low-Dimensional Life of Critical Anderson Electron
• Multifractality in monitored single-particle dynamics
• Critical behavior at the integer quantum Hall transition in a network model on the Kagome lattice
• Phase classification in the long-range Harper model using machine learning
• Topological Dimensions from Disorder and Quantum Mechanics?
• Quasiperiodicity-induced enhancement of superconductivity in one-dimensional critical systems
• Fractal Structure of Random Matrices
• Distribution of critical temperature at Anderson localization
• Spin-mixing-tunneling network model for Anderson transitions in two-dimensional disordered spinful electrons
• Renormalization Group Derivation of the Localization Length Exponent in the Integer Quantum Hall Effect
• Disorder-induced instability of a Weyl nodal loop semimetal towards a diffusive topological metal with protected multifractal surface states
• Spatial Structures of Anomalously Localized States in Tail Regions at the Anderson Transition
• Photonic Simulation of Localization Phenomena Using Boson Sampling
• Many-body spectral transitions through the lens of the variable-range SYK2 model
• Half metals at intermediate energy scales in Anderson-type insulators
• Quantum Fidelity of the Aubry-André Model and the Exponential Orthogonality Catastrophe
• Enhanced spin Hall effect in strong magnetic disorder
• Effect of spin-orbit coupling in one-dimensional quasicrystals with power-law hopping