Fluctuations of the inverse compressibility in disordered electron systems

We consider interacting electrons in one- and two-dimensional disordered sy stems and observe within the Hartree-Fock approximation that relative fluct uations of the inverse compressibility in general decrease with the hopping strength, signaling metal-insulator transitions in the systems. Particular ly, in one dimension the perturbative approach reveals two regimes where th e behaviors of the relative fluctuations with the system size are different : In the localized regime the relative fluctuations are independent of the size while in the opposite limit corresponding to the diffusive regime the relative fluctuations scale linearly with the system size. To check the val idity of the Hartree-Fock approximation, we also obtain exact results for s mall systems via the Lanczos method, which suggests that for intermediate v alues of the hopping strength the relative fluctuations are overestimated i n the Hartree-Fock approximation. [S0163-1829(99)02804-0].