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arXiv:0810.2450 · Physical Review B

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

Markus Holzmann, B. Bernu, Valério Olevano, Richard M. Martin, David M. Ceperley

Published Jan 30, 2009• 45 citations
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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 ${N}^{\ensuremath{-}1/4}$. These corrections dominate the extrapolation of the renormalization factor $Z$ and the single-particle effective mass ${m}^{\ensuremath{\ast}}$ to the infinite system size. We show how convergence can be improved using analytical corrections. In the range $1\ensuremath{\le}{r}_{s}\ensuremath{\le}10$, we get a lower renormalization factor $Z$ and a higher effective mass ${m}^{\ensuremath{\ast}}>m$ compared to the perturbative random-phase approximation values.

DOI
10.1103/physrevb.79.041308

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Excitations of the two-dimensional electron gas, including many-body effects, are calculated with a variational Monte Carlo method. Correlated sampling is introduced to calculate small energy differences between different excitations. The usual pair-product (Slater-Jastrow) trial wave function is found to lack certain correlations entirely so that backflow correlation is crucial. From the excitation energies calculated here, we determine Fermi-liquid parameters and related physical quantities such as the effective mass and the Land\'e g factor of the system. Our results for the effective mass are compared with previous analytic calculations.
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