Simple Classical Mapping of the Spin-Polarized Quantum Electron Gas: Distribution Functions and Local-Field Corrections

Dharma‐wardana, M. W. C.; Perrot, F.

doi:10.1103/physrevlett.84.959

Cited by 109 publications

(156 citation statements)

References 28 publications

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“…By supplementing that approach with our small-r expansions of Eqs. (22) and (23), it should be possible to find essentially-exact spin-resolved pairdistribution functions and correlation energies.…”

Section: Discussionmentioning

confidence: 99%

Short-range correlation in the uniform electron gas: Extended Overhauser model

2001

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We use the two-electron wavefunctions (geminals) and the simple screened Coulomb potential proposed by Overhauser [Can. J. Phys. 73, 683 (1995)] to compute the pair-distribution function g(r) for a uniform electron gas, finding the exact g(0) for this model and extending the results from g(0) to g(r). We find that the short-range (r < rs) part of this g(r) is in excellent agreement with Quantum Monte Carlo simulations for a wide range of electron densities. We are thus able to estimate the value of the second-order (r 2 ) coefficient of the small interelectronic-distance expansion of the pair-distribution function. The coefficients of the small-r expansion of the spin-resolved g σσ ′ (r) have density or rs dependences which we parametrize in a way that makes it easy to find their coupling-constant averages. Their spin-polarization or ζ dependences are estimated from a proposed spin scaling relation.

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Section: Discussionmentioning

confidence: 99%

Short-range correlation in the uniform electron gas: Extended Overhauser model

2001

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“…Finite-T Singwi-Tosi-Land-Sjölander (STLS) [22,23] local-field corrections allow for an extension to moderate coupling [23], but exhibit non-physical behavior at short distances for moderate to low densities, so improved expressions are highly needed. Further, quantum-classical mapping [24,25] allows for semi-quantitative descriptions of warm dense matter in limiting cases. Therefore, an accurate description of warm dense matter in general and of the warm dense UEG in particular can only be achieved using computational approaches, primarily quantum Monte-Carlo (QMC) methods which, however, are hampered by the fermion sign problem [28,29].…”

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confidence: 99%

Ab InitioQuantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit

et al. 2016

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We perform ab initio quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with linear response theory we are able to remove finite-size errors from the potential energy over the entire warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown et al. [PRL 110, 146405 (2013)]. Extensive new QMC results for up to N = 1000 electrons enable us to compute the potential energy V and the exchange-correlation free energy Fxc of the macroscopic electron gas with an unprecedented accuracy of |∆V |/|V |, |∆Fxc|/|F |xc ∼ 10 −3 . A comparison of our new data to the recent parametrization of Fxc by Karasiev et al. [PRL 112, 076403 (2014)] reveals significant deviations to the latter.The uniform electron gas (UEG), consisting of electrons on a uniform neutralizing background, is one of the most important model systems in physics [1]. Besides being a simple model for metals, the UEG has been central to the development of linear response theory and more sophisticated perturbative treatments of solids, the formulation of the concepts of quasiparticles and elementary excitations, and the remarkable successes of density functional theory.The practical application of ground-state density functional theory in condensed matter physics, chemistry and materials science rests on a reliable parametrization of the exchange-correlation energy of the UEG [2], which in turn is based on accurate quantum Monte Carlo (QMC) simulation data [3]. However, the charged quantum matter in astrophysical systems such as planet cores and white dwarf atmospheres [4,5] is at temperatures way above the ground state, as are inertial confinement fusion targets [6][7][8], laser-excited solids [9], and pressure induced modifications of solids, such as insulator-metal transitions [10,11]. This unusual regime, in which strong ionic correlations coexist with electronic quantum effects and partial ionization, has been termed "warm dense matter" and is one of the most active frontiers in plasma physics and materials science.The warm dense regime is characterized by the existence of two comparable length scales and two comparable energy scales. The length scales are the mean interparticle distance,r, and the Bohr radius, a 0 ; the energy scales are the thermal energy, k B T , and the electronic Fermi energy, E F . The dimensionless parameters [12] r s =r/a 0 and Θ = k B T /E F are of order unity. Because Θ ∼ 1, the use of ground-state density functional theory is inappropriate and extensions to finite T are indispensible; these require accurate exchange-correlation functionals for finite temperatures [13][14][15][16][17]. Because neither r s nor Θ is small, there are no small parameters, and weakcoupling expansions beyond Hartree-Fock such as the Montroll-Ward (MW) and e 4 (e4) approximations [18,19], as well as linear response theory within the random- phase approximation (RPA) break down [20,21]. Finite-T Singwi-Tosi-Land-Sjölander (STLS) [22,23] local-fiel...

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“…Given the V xc , the inhomogeneous density distribution around a given particle can be calculated, and the pairdistribution is deduced from it. QMC results in 2-D and 3-D electron systems, and shown to provide excellent agreement, even at the extreme quantum limit of zero temperature [13,18]. CHNC uses a "quantum temperature" T q , which depends on the Fermion density.…”

Section: A Hnc and Chnc Methodsmentioning

confidence: 99%

“…The objective of this paper is to study such 2T-2M plasmas using results from moleculardynamics (MD) [11], HNC [12], classical-map HNC (CHNC) [13,14], quantum Monte Carlo (QMC) [11] and Kohn-Sham (KS) [6] methods to establish the proper implementation of quantum effects and 2T, 2M situations in simulation studies. One of our main interests would be uniform hydrogenic plasmas free of bound states, in the regime of warm-dense matter.…”

Section: Introductionmentioning

confidence: 99%

Pair-distribution functions of two-temperature two-mass systems: Comparison of molecular dynamics, classical-map hypernetted chain, quantum Monte Carlo, and Kohn-Sham calculations for dense hydrogen

Dharma‐wardana

Murillo

2008

Phys. Rev. E

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Two-temperature, two-mass quasi-equilibrium plasmas may occur in electron-ion plasmas, nuclear-matter, as well as in electron-hole condensed-matter systems. Dense two-temperature hydrogen plasmas straddle the difficult partially-degenerate regime of electron densities and temperatures which are important in astrophysics, in inertial-confinement fusion research, and other areas of warm dense matter physics. Results from Kohn-Sham calculations and QMC are used to benchmark the procedures used in classical molecular-dynamics simulations, HNC and CHNC methods to derive electron-electron and electron-proton pair-distribution functions. Then, nonequilibrium molecular dynamics for two-temperature, two-mass plasmas are used to obtain the pair distribution. Using these results, the correct HNC and CHNC procedures for the evaluation of pair-distribution functions in two-temperature two-mass two-component charged fluids are established. Results for a mass ratio of 1:5, typical of electron-hole fluids, as well as for compressed hydrogen are presented.

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Simple Classical Mapping of the Spin-Polarized Quantum Electron Gas: Distribution Functions and Local-Field Corrections

Cited by 109 publications

References 28 publications

Short-range correlation in the uniform electron gas: Extended Overhauser model

Short-range correlation in the uniform electron gas: Extended Overhauser model

Ab InitioQuantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit

Pair-distribution functions of two-temperature two-mass systems: Comparison of molecular dynamics, classical-map hypernetted chain, quantum Monte Carlo, and Kohn-Sham calculations for dense hydrogen

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