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 $m^{\ast }$ to the infinite system size. We show how convergence can be improved using analytical corrections. In the range $1\le r_s\le 10$, we get a lower renormalization factor $Z$ and a higher effective mass $m^{\ast }>m$ compared to the perturbative random-phase approximation values.

• Received 16 December 2008

DOI:https://doi.org/10.1103/PhysRevB.79.041308