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 Wc for any nonzero value of the interaction strength. At the critical point the spacings distribution has a small- s behavior Pc(s)∝s, and a Poisson-like decay at large spacings.