Fluctuations of the inverse compressibility in disordered electron systems

We consider interacting electrons in one- and two-dimensional disordered systems and observe within the Hartree-Fock approximation that relative fluctuations of the inverse compressibility in general decrease with the hopping strength, signaling metal-insulator transitions in the systems. Particularly, in one dimension the perturbative approach reveals two regimes where the 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 validity of the Hartree-Fock approximation, we also obtain exact results for small systems via the Lanczos method, which suggests that for intermediate values of the hopping strength the relative fluctuations are overestimated in the Hartree-Fock approximation.