Finite-size error in many-body simulations with long-range interactions

We discuss the origin of the finite-size error of the energy in many-body simulation of systems of charged particles and we propose a correction based on the random-phase approximation at long wavelengths. The correction is determined mainly by the collective charge oscillations of the interacting system. Finite-size corrections, both on kinetic and potential energy, can be calculated within a single simulation. Results are presented for the electron gas and silicon.