Quantum ergodicity for electrons in two dimensions

We study the effect of electron-electron interaction on a two dimensional (2D) disordered lattice. For the case of two electrons the analytical estimates are presented showing a transition from localized to delocalized states in a way similar to the Anderson transition in 3D. The localized phase corresponds to large values of the parameter r_s, which is determined by the ratio of the Coulomb and Fermi energies. The numerical investigations of the spectral statistics P(s) in a system with up to N_p=30 spin polarized electrons show the transition from the Poisson to the Wigner-Dyson distribution at a total electron energy independent of N_p. The relation to experiments on the metal-insulator transition in 2D is also discussed.