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

Abstract

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 analytically. 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 RPA values.

4 pages, 3 figures

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