Ab Initio Quantum Monte Carlo Simulations of the Uniform Electron Gas without Fixed Nodes II: Unpolarized Case

TL;DR

This paper extends ab initio quantum Monte Carlo methods to unpolarized uniform electron gas, improving accuracy in thermodynamic property calculations and comparing results with previous data.

Contribution

It introduces enhancements to existing Monte Carlo approaches for unpolarized electron gas, enabling accurate simulations without fixed-node approximation.

Findings

Better agreement with previous exchange correlation energy data

Significant deviations in kinetic and potential energy contributions

Successful extension of methods to unpolarized case

Abstract

In a recent publication [S. Groth \textit{et al.}, PRB (2016)], we have shown that the combination of two novel complementary quantum Monte Carlo approaches, namely configuration path integral Monte Carlo (CPIMC) [T. Schoof \textit{et al.}, PRL \textbf{115}, 130402 (2015)] and permutation blocking path integral Monte Carlo (PB-PIMC) [T. Dornheim \textit{et al.}, NJP \textbf{17}, 073017 (2015)], allows for the accurate computation of thermodynamic properties of the spin-polarized uniform electron gas (UEG) over a wide range of temperatures and densities without the fixed-node approximation. In the present work, we extend this concept to the unpolarized case, which requires non-trivial enhancements that we describe in detail. We compare our new simulation results with recent restricted path integral Monte Carlo data [E. Brown \textit{et al}., PRL \textbf{110}, 146405 (2013)] for different energy contributions and pair distribution functions and find, for the exchange correlation energy, overall better agreement than for the spin-polarized case, while the separate kinetic and potential contributions substantially deviate.