Cm. Canali et al., DISTRIBUTION OF LEVEL CURVATURES FOR THE ANDERSON MODEL AT THE LOCALIZATION-DELOCALIZATION TRANSITION, Physical review. B, Condensed matter, 54(3), 1996, pp. 1431-1434
We compute the distribution function of single-level curvatures, P(k),
for a tight-binding model with site disorder, on a cubic lattice. In
metals P(k) is very close to the predictions of the random-matrix theo
ry (RMT). In insulators P(k) has a logarithmically normal form. At the
Anderson localization-delocalization transition P(k) fits very well t
he proposed novel distribution P(k)proportional to(1 + k(mu))(3/mu) wi
th mu approximate to 1.58, which approaches the RMT result for large k
and is nonanalytical at small k. We ascribe Such a nonanalyticity to
the spatial multifractality of the critical wave functions.