A Phaseless Auxiliary-Field Quantum Monte Carlo Perspective on the Uniform Electron Gas at Finite Temperatures: Issues, Observations, and Benchmark Study

TL;DR

This study assesses the accuracy of the phaseless finite temperature auxiliary field quantum Monte Carlo method for the uniform electron gas, revealing its strengths at high to intermediate densities and differences from zero-temperature approaches.

Contribution

It provides a detailed comparison of ph-FT-AFQMC with exact and coupled cluster results, highlighting its accuracy and differences from zero-temperature methods at finite temperatures.

Findings

ph-FT-AFQMC is accurate at high to intermediate densities.

It differs fundamentally from zero-temperature phaseless AFQMC.

Exchange-correlation energies agree well with existing parameterizations.

Abstract

We investigate the viability of the phaseless finite temperature auxiliary field quantum Monte Carlo (ph-FT-AFQMC) method for ab initio systems using the uniform electron gas as a model. Through comparisons with exact results and finite temperature coupled cluster theory, we find that ph-FT-AFQMC is sufficiently accurate at high to intermediate electronic densities. We show both analytically and numerically that the phaseless constraint at finite temperature is fundamentally different from its zero temperature counterpart (i.e., ph-ZT-AFQMC) and generally one should not expect ph-FT-AFQMC to agree with ph-ZT-AFQMC in the low temperature limit. With an efficient implementation, we are able to compare exchange-correlation energies to existing results in the thermodynamic limit and find that existing parameterizations are highly accurate. In particular, we found that ph-FT-AFQMC exchange-correlation energies are in a better agreement with a known parametrization than is restricted path-integral Monte Carlo in the regime of $\Theta\le0.5$ and $r_s \le 2$, which highlights the strength of ph-FT-AFQMC.