Pair-distribution functions of the two-dimensional electron gas

TL;DR

This paper introduces new analytical formulas for the pair-distribution functions and potential energy of the two-dimensional electron gas, derived from extensive quantum Monte Carlo simulations, aiding research in condensed matter physics and electronic structure.

Contribution

It provides the first accurate analytical representations of pair-distribution functions and potential energy for the 2D electron gas across various densities and spin polarizations.

Findings

Formulas accurately represent pair-distribution functions.

Negligible improvements from backflow correlations in simulations.

Useful for modeling semiconductor heterostructures and quantum dots.

Abstract

Based on its known exact properties and a new set of extensive fixed-node reptation quantum Monte Carlo simulations (both with and without backflow correlations, which in this case turn out to yield negligible improvements), we propose a new analytical representation of (i) the spin-summed pair-distribution function and (ii) the spin-resolved potential energy of the ideal two-dimensional interacting electron gas for a wide range of electron densities and spin polarization, plus (iii) the spin-resolved pair-distribution function of the unpolarized gas. These formulae provide an accurate reference for quantities previously not available in analytic form, and may be relevant to semiconductor heterostructures, metal-insulator transitions and quantum dots both directly, in terms of phase diagram and spin susceptibility, and indirectly, as key ingredients for the construction of new two-dimensional spin density functionals, beyond the local approximation.