# An Auxiliary-Field Quantum Monte Carlo Perspective on the Ground State of the Dense Uniform Electron Gas: An Investigation with Hartree-Fock Trial Wavefunctions

## TL;DR

This paper evaluates the effectiveness of Hartree-Fock trial wavefunctions in phaseless auxiliary-field quantum Monte Carlo for the uniform electron gas, demonstrating high accuracy for dense systems and highlighting challenges at lower densities.

## Contribution

It introduces and benchmarks the use of Hartree-Fock trial wavefunctions in ph-AFQMC for the uniform electron gas, providing new high-accuracy data and insights into their performance.

## Key findings

- RHF+ph-AFQMC is highly accurate for systems with $r_s \,\le\ 2.0$
- RHF+ph-AFQMC outperforms certain coupled-cluster methods for $r_s \,\le\ 3.0$
- Challenges remain for $r_s = 5.0$, indicating the need for better trial wavefunctions.

## Abstract

We assess the utility of Hartree-Fock (HF) trial wavefunctions in performing phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) on the uniform electron gas (UEG) model. The combination of ph-AFQMC with spin-restricted HF (RHF+ph-AFQMC), was found to be highly accurate and efficient for systems containing up to 114 electrons in 2109 orbitals, particularly for $r_s$ $\le$ 2.0. Compared to spin-restricted coupled-cluster (RCC) methods, we found that RHF+ph-AFQMC performs better than CC with singles, doubles, and triples (RCCSDT) and similarly to or slightly worse than CC with singles, doubles, triples, and quadruples (RCCSDTQ) for $r_s$ $\le$ 3.0 in the 14-electron UEG model. With the 54-electron, we found RHF+ph-AFQMC to be nearly exact for $r_s$ $\le$ 2.0 and pointed out potential biases in existing benchmarks. Encouraged by these, we performed RHF+ph-AFQMC on the 114-electron UEG model for $r_s$ $\le$ 2.0 and provided new benchmark data for future method development. We found that the UEG models with $r_s$ = 5.0 remain to be challenging for RHF+ph-AFQMC. Employing non-orthogonal configuration expansions or unrestricted HF states as trial wavefunctions was also found to be ineffective in the case of the 14-electron UEG model with $r_s$ = 5.0. We emphasize the need for a better trial wavefunction for ph-AFQMC in simulating strongly correlated systems. With the 54-electron and 114-electron UEG models, we stress the potential utility of RHF+ph-AFQMC for simulating dense solids.