Density modulations and addition spectra of interacting electrons in disordered quantum dots

We analyze the ground state of spinless fermions on a lattice in a weakly d isordered potential, interacting via a nearest-neighbor interaction, by app lying the self-consistent Hartree-Fock approximation. We find that charge d ensity modulations emerge progressively when r(s) greater than or similar t o 1, even away from half-filling, with only short-range density correlation s. Classical geometry-dependent magic numbers can show up in the addition s pectrum which are remarkably robust against quantum fluctuations and disord er averaging.