Multifractality of Hamiltonians with power-law transfer terms

Abstract

Finite-size effects in the generalized fractal dimensions $d_q$ are investigated numerically. We concentrate on a one-dimensional disordered model with long-range random hopping amplitudes in both the strong- and the weak-coupling regime. At the macroscopic limit, a linear dependence of $d_q$ on $q$ is found in both regimes for values of $q \alt 4g^{-1}$, where $g$ is the coupling constant of the model.

arXiv commentRevTex4, 5 two-column pages, 5 .eps figures, to be published in Phys. Rev. B

References in corpus (25)

• Scaling Theory of the Integer Quantum Hall Effect
• Statistics of energy levels and eigenfunctions in disordered systems
• Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
• Fluctuations of the inverse participation ratio at the Anderson transition
• Multifractality and critical fluctuations at the Anderson transition
• Glass transition of a particle in a random potential, front selection in nonlinear RG and entropic phenomena in Liouville and SinhGordon models
• Mutifractal Analysis of Broadly Distributed Observables at Criticality
• New Class of Random Matrix Ensembles with Multifractal Eigenvectors
• Gaussian field theories, random Cantor sets and multifractality
• Exact calculation of multifractal exponents of the critical wave function of Dirac fermions in a random magnetic field
• Multifractality: generic property of eigenstates of 2D disordered metals.
• Towards a Field Theory of the Plateau Transition
• Impurity States and the Absence of Quasiparticle Localization in Disordered D-Wave Superconductors
• 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
• Energy level dynamics in systems with weakly multifractal eigenstates: equivalence to 1D correlated fermions
• Dielectric resonances of binary random networks
• A new model of quantum chaotic billiards: Spectral Statistics and Wavefunctions in 2D
• $f(\alpha )$ Multifractal spectrum at strong and weak disorder
• Critical spectral statistics in two-dimensional interacting disordered systems
• Anomalously large critical regions in power-law random matrix ensembles
• Metal-insulator transition in two-dimensional disordered systems with power-law transfer terms
• Critical generalized inverse participation ratio distributions

Cited by in corpus (24)

• Anderson Transitions
• Exact relations between multifractal exponents at the Anderson transition
• Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model
• Dimensional dependence of the metal-insulator transition
• A semiclassical theory of the Anderson transition
• Non-Hermitian Aubry-André model with Power-Law Hopping
• Chiral phase transition and Anderson localization in the Instanton Liquid Model for QCD
• Level-statistics in Disordered Systems: A single parametric scaling and Connection to Brownian Ensembles
• Boundary multifractality in critical 1D systems with long-range hopping
• Differentiable potentials and metallic states in disordered one-dimensional systems
• Anomalous multifractality in quantum chains with strongly correlated disorder
• Semi-Poisson statistics in quantum chaos
• Power spectrum for critical statistics: A novel spectral characterization of the Anderson transition
• Power law hopping of single particles in one-dimensional non-Hermitian quasicrystals
• A critical Dyson hierarchical model for the Anderson localization transition
• Long-range hopping in a quasiperiodic potential weakens the non-Hermitian skin effect
• Criticality in the Quantum Kicked Rotor with a Smooth Potential
• Two-level correlation function of critical random-matrix ensembles
• Critical properties in long-range hopping Hamiltonians
• Critical level spacing distribution in long-range hopping Hamiltonians
• Unraveling Multifractality and Mobility Edges in Quasiperiodic Aubry-André-Harper Chains through High-Harmonic Generation
• Criticality without self-similarity: a 2D system with random long-range hopping
• Effect of a magnetic flux on the critical behavior of a system with long range hopping
• Statistical properties of the critical eigenstates in power-law random banded matrices across the band