Distribution of level curvatures for the Anderson model at the localization-delocalization transition

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 theory (RMT). In insulators P(k) has a logarithmically normal form. At the Anderson localization-delocalization transition P(k) fits very well the proposed novel distribution P(k)proportional to(1 + k(mu))(3/mu) with 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.