Renormalization factor and effective mass of the two-dimensional electron gas

We calculate the momentum distribution of the Fermi-liquid phase of the homogeneous two-dimensional electron gas. We show that close to the Fermi surface, the momentum distribution of a finite system with N electrons approaches its thermodynamic limit slowly, with leading-order corrections scaling as N^-1/4. These corrections dominate the extrapolation of the renormalization factor Z and the single-particle effective mass m^ to the infinite system size. We show how convergence can be improved using analytical corrections. In the range 1≤rₛ≤10, we get a lower renormalization factor Z and a higher effective mass m^>m compared to the perturbative random-phase approximation values.