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 Θ ≤ 0.5 and rs ≤ 2, which highlights the strength of ph-FT-AFQMC.

Spectral Functions from Auxiliary-Field Quantum Monte Carlo without Analytic Continuation: The Extended Koopmans’ Theorem Approach

“…AFQMC has emerged as a unique tool for simulating correlated solids. 55,57,60,63,101 A model solid that describes the basic physics of metallic systems is the UEG. The accuracy and scope of AFQMC in studying the finite-basis supercell model of UEG has been well documented at zero temperature and finite temperature.…”

Analytical representation of the Local Field Correction of the Uniform Electron Gas within the Effective Static Approximation

“…One way towards this goal would be the development of new fermionic QMC approaches at finite temperature, to estimate the imaginary-time density-density correlation function F (q, τ )-the crucial ingredient for the reconstruction of both S(q, ω) and G(q, ω). Here the phaseless auxiliary-field QMC method constitutes a promising candidate [67].…”

“…This challenge has resulted in a substantial progress regarding the development of electronic QMC simulations at WDM conditions [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69], which ultimately led to the first parametrizations of the XC-free energy f xc of the UEG [70,71], allowing for thermal DFT calculations on the level of the local density approximation (LDA). At the same time, DFT approaches are being developed that deal efficiently with the drastic increase in the basis size for high temperatures [72][73][74][75][76], and even gradient corrections to the LDA have become available [50,77].…”

Overcoming finite-size effects in electronic structure simulations at extreme conditions

“…The final part of the investigation in this work is devoted to the performance of our new FSC scheme for low temperatures. This is a particularly interesting regime, as accurate QMC data for the UEG are sparse at these conditions due to the fermion sign problem [13,44,55,57]. In addition, the UEG has attracted renewed interest at high densities also in the groundstate [91,92], where the full configuration interaction QMC (FCIQMC) method [93] is capable to give accurate results for finite N .…”

“…This interest has sparked a series of new developments in the field of electronic QMC simulations at finite temperature [26,32,33,[42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57], which, in turn, has caused the need to understand the impact of thermal excitations on finite-size effects. In general, this problem can be re-stated as the search for a short-range property that can be accurately inferred from a QMC simulation of a finite-system and, in combination with a readily available theory such as the random phase approximation (RPA) [see Eq.…”