The Level Spacing Distribution Near the Anderson Transition
Abstract
For a disordered system near the Anderson transition we show that the nearest-level-spacing distribution has the asymptotics
P(s)∝exp(−A
s
2−γ
)
for $s\gg \av{s}\equiv 1$ which is universal and intermediate between the Gaussian asymptotics in a metal and the Poisson in an insulator. (Here the critical exponent
0<γ<1
and the numerical coefficient
A
depend only on the dimensionality
d>2
). It is obtained by mapping the energy level distribution to the Gibbs distribution for a classical one-dimensional gas with a pairwise interaction. The interaction, consistent with the universal asymptotics of the two-level correlation function found previously, is proved to be the power-law repulsion with the exponent
−γ
.