Universal Spectral Correlations at the Mobility Edge
Abstract
We demonstrate the level statistics in the vicinity of the Anderson transition in
d>2
dimensions to be universal and drastically different from both Wigner-Dyson in the metallic regime and Poisson in the insulator regime. The variance of the number of levels
N
in a given energy interval with
⟨N⟩≫1
is proved to behave as
⟨N
⟩
γ
where
γ=1−(νd
)
−1
and
ν
is the correlation length exponent. The inequality
γ<1
, shown to be required by an exact sum rule, results from nontrivial cancellations (due to the causality and scaling requirements) in calculating the two-level correlation function.