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 parameter rs, 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 Np = 30 spin polarized electrons show the transition from the Poisson to the Wigner-Dyson distribution at a total electron energy independent of Np. The relation to the experiments on metal-insulator transition in 2D is also discussed.