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

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 $\Theta \le 0.5$ and $r_s\le 2$, which highlights the strength of ph-FT-AFQMC.

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Cited by in corpus (5)

• Analytical representation of the Local Field Correction of the Uniform Electron Gas within the Effective Static Approximation
• Nonlinear density response from imaginary-time correlation functions: Ab initio path integral Monte Carlo simulations of the warm dense electron gas
• Overcoming finite-size effects in electronic structure simulations at extreme conditions
• Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, grand canonical and canonical ensembles
• Density-Functional-Theory Perspective on the Non-Linear Response of Correlated Electrons Across Temperature Regimes