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

Spink, G. G.; Needs, R. J.; Drummond, Neil

doi:10.1103/physrevb.88.085121

Cited by 107 publications

(143 citation statements)

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“…It approximates the local XC energy per particle, ε xc , as the value for the HEG at the local density, ε LDA xc (n(r)) ≈ ε HEG xc (n)| n=n(r) [also see Eq. (3) [5] for the spin-polarized T = 0 K HEG also validate the spininterpolation formulae used in that case, the local spin density approximation (LSDA). All more refined ε xc approximations reduce to the LSDA in the weak inhomogeneity limit.…”

Section: Pacs Numbersmentioning

confidence: 99%

“…Computational implementation is via parametrizations [2,3] of HEG quantum Monte Carlo (QMC) data [4]. Recent QMC results [5] for the spin-polarized T = 0 K HEG also validate the spininterpolation formulae used in that case, the local spin density approximation (LSDA). All more refined ε xc approximations reduce to the LSDA in the weak inhomogeneity limit.…”

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confidence: 99%

“…Their parametrization used classical map hypernetted chain data for the HEG and proper behavior as T → 0 K. We have reparametrized φ(r s , t, ζ) using the more recent T = 0 K QMC data (which includes intermediate polarizations ζ = 0.34, 0.66) [5] along with the CHNC data for intermediate ζ = 0.6 in Table IV Table III. The value of g 1 is fixed from the condition that lim rs→0 φ(r s , t = 0, ζ) = φ(ζ).…”

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Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations

et al. 2014

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An accurate analytical parametrization for the exchange-correlation free energy of the homogeneous electron gas, including interpolation for partial spin-polarization, is derived via thermodynamic analysis of recent restricted path integral Monte-Carlo (RPIMC) data. This parametrization constitutes the local spin density approximation (LSDA) for the exchange-correlation functional in density functional theory. The new finite-temperature LSDA reproduces the RPIMC data well, satisfies the correct high-density and low-and high-T asymptotic limits, and is well-behaved beyond the range of the RPIMC data, suggestive of broad utility. PACS numbers:The homogeneous electron gas (HEG) is a fundamentally important system for understanding many-fermion physics. In the absence of exact analytical solutions for its energetics, high-precision numerical results have been critical to insight. Recently published [1] restricted path integral Monte Carlo (RPIMC) data for the HEG over a wide range of temperatures and densities open the opportunity to obtain closed form expressions for HEG thermodynamics, in particular the exchange and correlation (XC) contributions. Such expressions extracted from Monte Carlo data are well-known for the zero-T HEG, where they have played a major role in understanding inhomogeneous electron-system behavior. We provide the corresponding thermodynamical expressions for wide temperature and density ranges.Density functional theory (DFT) is the motivating context. For ground-state DFT, the most basic exchangecorrelation (XC) density functional is the local density approximation (LDA). It approximates the local XC energy per particle, ε xc , as the value for the HEG at the local density, ε LDA xc (n(r)) ≈ ε HEG xc (n)| n=n(r) [also see Eq. (3) [5] for the spin-polarized T = 0 K HEG also validate the spininterpolation formulae used in that case, the local spin density approximation (LSDA). All more refined ε xc approximations reduce to the LSDA in the weak inhomogeneity limit.Finite-temperature DFT [6-8] increasingly is being used to study matter under diverse density and temperature conditions [9][10][11][12][13][14]. In it, the XC free-energy is defined by decomposition of the universal free-energy density functional (independent of the external potential). With the T -dependence suppressed for now, that functional isThe first two terms are the non-interacting kinetic energy and entropy (also known as the Kohn-Sham KE and entropy), F H [n] is the classical electron-electron Coulomb energy, and the XC free energy by definition iswith T [n] and S[n] the interacting system kinetic energy and entropy and U ee [n] the full quantum mechanical electron-electron interaction energy. Just as for T = 0 K, the existence theorems of finite-T DFT are not constructive for F xc , so approximations must be devised. Common practice [9] in simulations is to use a. This gives only the implicit T -dependence provided by n(r, T ). However, there is substantial evidence from both finite-T Hartree-Fock [12,15] and finite-T exac...

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Section: Pacs Numbersmentioning

confidence: 99%

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Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations

et al. 2014

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“…We shall address these questions by accurately determiningω ex (q), "the oscillator strength" of the pole f ex (q), and S(q, ω) for r s from r c s up to about 20 in which the ground state has already been confirmed to be a paramagnetic metal. 6 A straightforward way of obtaining accurate results for S(q, ω) is to perform the highly self-consistent calculation in the GWΓ scheme 22 which includes the vertex function Γ satisfying the Ward identity (WI), 23,24 just as done for S(q, ω) for r s ≤ 5, 25 but it turns out that this GWΓ does not work well in the dielectric-catastrophe regime. Thus it is revised into the GWΓ WI scheme 10,26 to obtain the self-consistent results for S(q, ω) as well as n(p) up to r s = 10, but there still remains the problem of reaching a fully self-consistent solution for r s > 10.…”

Section: Introductionmentioning

confidence: 99%

“…The diffusion Monte Carlo (DMC) calculations are done to analyze the ground-state phases, including spin polarization, in the wide range of r s 5 and recently for 0.5 ≤ r s ≤ 20 in more detail 6 , but we do not know the precise behavior of other physical quantities, such as the momentum distribution function n(p) for r s > 5. It is true that some quantum Monte Carlo calculations are done to obtain n(p) for r s ≤ 10, 7,8 but the results are not very accurate due probably to large size effects and improper starting trial functions, judging from the assessment of their accuracy by the sum rules for n(p).…”

Section: Introductionmentioning

confidence: 99%

Emergence of an excitonic collective mode in the dilute electron gas

Takada

2016

Phys. Rev. B

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By comparing two expressions for the polarization function Π(q, iω) given in terms of two different local-field factors, G+(q, iω) and Gs(q, iω), we have derived the kinetic-energy-fluctuation (or sixthpower) sum rule for the momentum distribution function n(p) in the three-dimensional electron gas. With use of this sum rule, together with the total-number (or second-power) and the kinetic-energy (or fourth-power) sum rules, we have obtained n(p) in the low-density electron gas at negative compressibility (namely, rs > 5.25 with rs being the conventional density parameter) up to rs ≈ 22 by improving on the interpolation scheme due to Gori-Giorge and Ziesche proposed in 2002. The obtained results for n(p) combined with the improved form for Gs(q, ω + i0 + ) are employed to calculate the dynamical structure factor S(q, ω) to reveal that a giant peak, even bigger than the plasmon peak, originating from an excitonic collective mode made of electron-hole pair excitations, emerges in the low-ω region at |q| near 2pF (pF: the Fermi wave number). Connected with this mode, we have discovered a singular point in the retarded dielectric function at ω = 0 and |q| ≈ 2pF.

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Free energy of the uniform electron gas: Testing analytical models against first‐principles results

Groth

Dornheim

Bönitz

2017

Contributions to Plasma Physics

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The uniform electron gas is a key model system in the description of matter, including dense plasmas and solid‐state systems. However, the simultaneous occurrence of quantum, correlation, and thermal effects makes the theoretical description challenging. For these reasons, over the last half century, many analytical approaches have been developed, the accuracy of which has remained unclear. We have recently obtained the first ab initio data for the exchange correlation free energy of the uniform electron gas, which now provides the opportunity to assess the quality of the mentioned approaches and parameterizations. Particular emphasis is placed on the warm, dense matter regime, where we find significant discrepancies between the different approaches.

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

Cited by 107 publications

References 56 publications

Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations

Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations

Emergence of an excitonic collective mode in the dilute electron gas

Free energy of the uniform electron gas: Testing analytical models against first‐principles results

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