First principles many-body approach to electron gas

We describe a first principles approach of constructing low energy, effective lattice model for the electron gas in a continuum of 2 and 3 spatial dimensions. The effects of the higher energy, unoccupied states are taken into account through virtue particle-hole excitations which screen the effective interactions at low energies. Using this effective model we obtain the correct order of magnitudes of the average inter- electron distance ($R_s$) at which the metal-insulator transition happens in 2d and 3d.