Critical level statistics at the Anderson transition in four-dimensional disordered systems
arXiv:cond-mat/9810286 · doi:10.1002/(SICI)1521-3889(199811)7:5/6<442::AID-ANDP442>3.0.CO;2-D
Abstract
The level spacing distribution is numerically calculated at the disorder-induced metal--insulator transition for dimensionality d=4 by applying the Lanczos diagonalisation. The critical level statistics are shown to deviate stronger from the result of the random matrix theory compared to those of d=3 and to become closer to the Poisson limit of uncorrelated spectra. Using the finite size scaling analysis for the probability distribution Q_n(E) of having n levels in a given energy interval E we find the critical disorder W_c = 34.5 \pm 0.5, the correlation length exponent ν= 1.1 \pm 0.2 and the critical spectral compressibility k_c \approx 0.5.
10 pages, LaTeX2e, 7 fig, invited talk at PILS (Percolation, Interaction, Localization: Simulations of Transport in Disordered Systems) Berlin, Germany 1998, to appear in Annalen der Physik
Cited by in corpus (26)
- 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
- Critical behavior at the localization transition on random regular graphs
- Dimensionality dependence of the wave function statistics at the Anderson transition
- Dimensional dependence of the metal-insulator transition
- Localization transition on complex networks via spectral statistics
- Energy level dynamics in systems with weakly multifractal eigenstates: equivalence to 1D correlated fermions
- Energy-level statistics at the metal-insulator transition in anisotropic systems
- A semiclassical theory of the Anderson transition
- Dimensional Dependence of Critical Exponent of the Anderson Transition in the Orthogonal Universality Class
- Chiral Random Matrix Model for Critical Statistics
- Quantum computation of the Anderson transition in presence of imperfections
- Multifractality at non-Anderson disorder-driven transitions in Weyl semimetals and other systems
- Study of the Localization Transition on a Cayley-tree via Spectral Statistics
- Low energy transition in spectral statistics of 2D interactingfermions
- Strong-disorder renormalization group study of the Anderson localization transition in three and higher dimensions
- Universal level-spacing statistics in quasiperiodic tight-binding models
- Analytical realization of finite-size scaling for Anderson localization: Is there transition in the 2D case?
- Universal conductance fluctuations in non-integer dimensions
- Two-level correlation function of critical random-matrix ensembles
- Finite-size scaling from self-consistent theory of localization
- Interpretation of high-dimensional numerical results for Anderson transition
- Scaling for level statistics from self-consistent theory of localization
- Analytical realization of finite-size scaling for Anderson localization. Does the band of critical states exist for d>2?
- Spectral properties of three-dimensional Anderson model