Exchange-correlation energy for the three-dimensional homogeneous electron gas at arbitrary temperature

We have studied the spin-polarized three-dimensional homogeneous electron gas using the diffusion quantum Monte Carlo method, with trial wave functions including backflow and three-body correlations in the Jastrow factor, and we have used twist averaging to reduce finite-size effects. Calculations of the pair-correlation function, including the on-top pair density, as well as the structure factor and the total energy, are reported for systems of 118 electrons in the density range r s = 0.5-20 a.u., and for spin polarizations of 0, 0.34, 0.66, and 1. We consider the spin resolution of the pair-correlation function and structure factor, and the energy of spin polarization. We show that a control variate method can reduce the variance when twist averaging, and we have achieved higher accuracy and lower noise than earlier quantum Monte Carlo studies.

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“…Recently, we became aware of complementary, finite-temperature results for the warm-dense HEG in the paper by E. W. Brown et al 49 …”

Section: Discussionmentioning

confidence: 99%

Quantum Monte Carlo study of the three-dimensional spin-polarized homogeneous electron gas

2013

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“…[24] w ere done w ith ju st 33 particles per spin projection, and the authors subsequently em ployed a com plex finite-size-scaling procedure. We note that this issue is still unresolved, and subsequent works applied very different finite-size scalings to the RPIM C data [25,29,30]. Thus, the question o f reliable high-tem perature data for the uniform electron gas at high densities remains.…”

Section: Introductionmentioning

confidence: 94%

“…In expressions (25) and (29) and related calculations, we now replace the potential Oa/,(xn6; P) with < & ab(.xab\P), thereby accounting for PBC effects. Note that one has to add to the first term in curly brackets in Eq.…”

Section: Gobi**- P) = a < T> Ab(xab; P) + (30)mentioning

confidence: 99%

Fermionic path-integral Monte Carlo results for the uniform electron gas at finite temperature

et al. 2015

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The uniform electron gas (UEG) at finite temperature has recently attracted substantial interest due to the experimental progress in the field of warm dense matter. To explain the experimental data, accurate theoretical models for high-density plasmas are needed that depend crucially on the quality of the thermodynamic properties of the quantum degenerate nonideal electrons and of the treatment of their interaction with the positive background. Recent fixed-node path-integral Monte Carlo (RPIMC) data are believed to be the most accurate for the UEG at finite temperature, but they become questionable at high degeneracy when the Brueckner parameter rs=a/aB--the ratio of the mean interparticle distance to the Bohr radius--approaches 1. The validity range of these simulations and their predictive capabilities for the UEG are presently unknown. This is due to the unknown quality of the used fixed nodes and of the finite-size scaling from N=33 simulated particles (per spin projection) to the macroscopic limit. To analyze these questions, we present alternative direct fermionic path integral Monte Carlo (DPIMC) simulations that are independent from RPIMC. Our simulations take into account quantum effects not only in the electron system but also in their interaction with the uniform positive background. Also, we use substantially larger particle numbers (up to three times more) and perform an extrapolation to the macroscopic limit. We observe very good agreement with RPIMC, for the polarized electron gas, up to moderate densities around rs=4, and larger deviations for the unpolarized case, for low temperatures. For higher densities (high electron degeneracy), rs≲1.5, both RPIMC and DPIMC are problematic due to the increased fermion sign problem.

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“…[21,22,25,[47][48][49]. It is defined as the difference between the total energy of the correlated system and the ideal energy U 0 ,…”

Section: A Exchange Correlation Energymentioning

confidence: 99%

Ab initioquantum Monte Carlo simulations of the uniform electron gas without fixed nodes: The unpolarized case

et al. 2016

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In a recent publication [S. Groth et al., PRB (2016)], we have shown that the combination of two novel complementary quantum Monte Carlo approaches, namely configuration path integral Monte Carlo (CPIMC) [T. Schoof et al., PRL 115, 130402 (2015)] and permutation blocking path integral Monte Carlo (PB-PIMC) [T. Dornheim et al., NJP 17, 073017 (2015)], allows for the accurate computation of thermodynamic properties of the spin-polarized uniform electron gas (UEG) over a wide range of temperatures and densities without the fixed-node approximation. In the present work, we extend this concept to the unpolarized case, which requires non-trivial enhancements that we describe in detail. We compare our new simulation results with recent restricted path integral Monte Carlo data [E. Brown et al., PRL 110, 146405 (2013)] for different energy contributions and pair distribution functions and find, for the exchange correlation energy, overall better agreement than for the spin-polarized case, while the separate kinetic and potential contributions substantially deviate.

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Exchange-correlation energy for the three-dimensional homogeneous electron gas at arbitrary temperature

Cited by 60 publications

References 42 publications

Quantum Monte Carlo study of the three-dimensional spin-polarized homogeneous electron gas

Quantum Monte Carlo study of the three-dimensional spin-polarized homogeneous electron gas

Fermionic path-integral Monte Carlo results for the uniform electron gas at finite temperature

Ab initioquantum Monte Carlo simulations of the uniform electron gas without fixed nodes: The unpolarized case

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