Correlation energies of the high-density spin-polarized electron gas to meV accuracy

TL;DR

This paper accurately calculates the correlation energies of high-density spin-polarized electron gas using advanced quantum Monte Carlo methods, revealing discrepancies with existing parametrizations and providing improved estimates at specific densities.

Contribution

It introduces a novel combination of quantum Monte Carlo techniques with finite size extrapolation to precisely determine correlation energies in the thermodynamic limit.

Findings

Correlation energies at $r_s=0.5$ and $1$ are determined to meV accuracy.

Fixed-node error exceeds 1 mHa, affecting results.

Perdew-Wang parametrization underestimates correlation energy by up to 6 meV.

Abstract

We present a novel combination of quantum Monte Carlo methods and a finite size extrapolation framework with which we calculate the thermodynamic limit of the exact correlation energy of the polarized electron gas at high densities to meV accuracy, $-40.44(5)$ and $-31.70(4)$ mHa at $r_{\rm s}=0.5$ and $1$, respectively. The fixed-node error is characterized and found to exceed $1$ mHa, and we show that the magnitude of the correlation energy of the polarized electron gas is underestimated by up to $6$ meV by the Perdew-Wang parametrization, for which we suggest improvements.