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 1rs10, we get a lower renormalization factor Z and a higher effective mass mm compared to the perturbative random-phase approximation values. The Fermi-liquid theory of Landau 1 postulates a one-toone mapping of low-energy excitations of an interacting quantum system with that of an ideal Fermi gas via the distribution function of quasiparticles of momentum k. The resulting energy functional has been successfully applied to describe equilibrium and transport properties of quantum Fermi liquids: the most prominent are the electron gas and liquid 3 He. 2,3 However, quantitative microscopic calculations of its basic ingredients, the renormalization factor Z, and the effective mass m remain challenging. In this Rapid Communication, we calculate these parameters for the two-dimensional electron gas 2DEG using quantum Monte Carlo QMC in the region 1rs10,