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 disordered potential, interacting via a nearest-neighbor interaction, by applying the self-consistent Hartree-Fock approximation. We find that charge density modulations emerge progressively when $r_s\gtrsim 1$, even away from half-filling, with only short-range density correlations. Classical geometry-dependent magic numbers can show up in the addition spectrum which are remarkably robust against quantum fluctuations and disorder averaging.