33 research outputs found
Crossover of Level Statistics between Strong and Weak Localization in Two Dimensions
We investigate numerically the statistical properties of spectra of
two-dimensional disordered systems by using the exact diagonalization and
decimation method applied to the Anderson model. Statistics of spacings
calculated for system sizes up to 1024 1024 lattice sites exhibits a
crossover between Wigner and Poisson distributions. We perform a self-contained
finite-size scaling analysis to find a single-valued one-parameter function
which governs the crossover. The scaling parameter is
deduced and compared with the localization length. does {\em
not} show critical behavior and has two asymptotic regimes corresponding to
weakly and strongly localized states.Comment: 4 pages in revtex, 3 postscript figure
Finite-size scaling from self-consistent theory of localization
Accepting validity of self-consistent theory of localization by Vollhardt and
Woelfle, we derive the finite-size scaling procedure used for studies of the
critical behavior in d-dimensional case and based on the use of auxiliary
quasi-1D systems. The obtained scaling functions for d=2 and d=3 are in good
agreement with numerical results: it signifies the absence of essential
contradictions with the Vollhardt and Woelfle theory on the level of raw data.
The results \nu=1.3-1.6, usually obtained at d=3 for the critical exponent of
the correlation length, are explained by the fact that dependence L+L_0 with
L_0>0 (L is the transversal size of the system) is interpreted as L^{1/\nu}
with \nu>1. For dimensions d\ge 4, the modified scaling relations are derived;
it demonstrates incorrectness of the conventional treatment of data for d=4 and
d=5, but establishes the constructive procedure for such a treatment.
Consequences for other variants of finite-size scaling are discussed.Comment: Latex, 23 pages, figures included; additional Fig.8 is added with
high precision data by Kramer et a
Critical level spacing distribution of two-dimensional disordered systems with spin-orbit coupling
The energy level statistics of 2D electrons with spin-orbit scattering are
considered near the disorder induced metal-insulator transition. Using the Ando
model, the nearest-level-spacing distribution is calculated numerically at the
critical point. It is shown that the critical spacing distribution is size
independent and has a Poisson-like decay at large spacings as distinct from the
Gaussian asymptotic form obtained by the random-matrix theory.Comment: 7 pages REVTeX, 2 uuencoded, gzipped figures; J. Phys. Condensed
Matter, in prin
Asymptotics of Universal Probability of Neighboring Level Spacings at the Anderson Transition
The nearest-neighbor level spacing distribution is numerically investigated
by directly diagonalizing disordered Anderson Hamiltonians for systems of sizes
up to 100 x 100 x 100 lattice sites. The scaling behavior of the level
statistics is examined for large spacings near the delocalization-localization
transition and the correlation length exponent is found. By using
high-precision calculations we conjecture a new interpolation of the critical
cumulative probability, which has size-independent asymptotic form \ln I(s)
\propto -s^{\alpha} with \alpha = 1.0 \pm 0.1.Comment: 5 pages, RevTex, 4 figures, to appear in Physical Review Letter
Scaling of Level Statistics at the Disorder-Induced Metal-Insulator Transition
The distribution of energy level separations for lattices of sizes up to
282828 sites is numerically calculated for the Anderson model.
The results show one-parameter scaling. The size-independent universality of
the critical level spacing distribution allows to detect with high precision
the critical disorder . The scaling properties yield the critical
exponent, , and the disorder dependence of the correlation
length.Comment: 11 pages (RevTex), 3 figures included (tar-compressed and uuencoded
using UUFILES), to appear in Phys.Rev. B 51 (Rapid Commun.
Critical spectral statistics in two-dimensional interacting disordered systems
The effect of Coulomb and short-range interactions on the spectral properties
of two-dimensional disordered systems with two spinless fermions is
investigated by numerical scaling techniques. The size independent universality
of the critical nearest level-spacing distribution allows one to find a
delocalization transition at a critical disorder for any non-zero
value of the interaction strength. At the critical point the spacings
distribution has a small- behavior , and a Poisson-like
decay at large spacings.Comment: 4 two-column pages, 3 eps figures, RevTeX, new results adde
Critical Level Statistics in Two-dimensional Disordered Electron Systems
The level statistics in the two dimensional disordered electron systems in
magnetic fields (unitary ensemble) or in the presence of strong spin-orbit
scattering (symplectic ensemble) are investigated at the Anderson transition
points. The level spacing distribution functions 's are found to be
independent of the system size or of the type of the potential distribution,
suggesting the universality. They behave as in the small region in
the former case, while rise is seen in the latter.Comment: LaTeX, to be published in J. Phys. Soc. Jpn. (Letter) Nov., Figures
will be sent on reques