Critical spectral statistics in two-dimensional interacting disordered systems

The effect of Coulomb and short-range interactions on the spectral properties of two-dimensional disordered systems with two spinless fermions is investigated by numerical scaling techniques. The size independent universality of the critical nearest level-spacing distribution $P(s)$ allows one to find a delocalization transition at a critical disorder $W_{\rm c}$ for any non-zero value of the interaction strength. At the critical point the spacings distribution has a small-$s$ behavior $P_c(s)\propto s$, and a Poisson-like decay at large spacings.