A Full Configuration Interaction Perspective on the Homogeneous Electron Gas

TL;DR

This paper introduces a stochastic Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method that achieves highly accurate energies for the homogeneous electron gas, surpassing previous methods in certain regimes.

Contribution

The paper presents a novel FCIQMC approach that samples the exact wavefunction in a large basis, providing more accurate energies for the HEG than prior techniques.

Findings

Achieved lower energy estimates than previous methods for 54-electron HEG at r_s=0.5 a.u.

Successfully extrapolated to remove basis set errors at r_s=1.0 a.u.

Demonstrated the viability of FCIQMC for accurate large-scale periodic systems.

Abstract

Highly accurate results for the homogeneous electron gas (HEG) have only been achieved to date within a diffusion Monte Carlo (DMC) framework. Here, we introduce a newly developed stochastic technique, Full Configuration Interaction Quantum Monte Carlo (FCIQMC), which samples the exact wavefunction expanded in plane wave Slater determinants. Despite the introduction of a basis set incompleteness error, we obtain a finite-basis energy which is significantly, and variationally lower than any previously published work for the 54-electron HEG at $r_s$ = 0.5 a.u., in a Hilbert space of $10^{108}$ Slater determinants. At this value of $r_s$, as well as of 1.0 a.u., we remove the remaining basis set incompleteness error by extrapolation, yielding results comparable or better than state-of-the-art DMC backflow energies. In doing so, we demonstrate that it is possible to yield highly accurate results with the FCIQMC method in sizable periodic systems.