The uniform electron gas

Loos, Pierre‐François; Gill, Peter M. W.

doi:10.1002/wcms.1257

Cited by 145 publications

(120 citation statements)

References 149 publications

(325 reference statements)

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“…The uniform electron gas (UEG) is one of the most fundamental model systems in physics [4,92,93]. In particular, the accurate parametrization [94,95] of the ground-state exchange-correlation energy e xc (r s ), based on ab inito quantum Monte Carlo simulations [96], has been essential for the striking success of density functional theory.…”

Section: A Summary Of Ab Initio Static Resultsmentioning

confidence: 99%

Ab initio simulation of warm dense matter

et al. 2020

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Warm dense matter (WDM) -an exotic state of highly compressed matter -has attracted high interest in recent years in astrophysics and for dense laboratory systems. At the same time, this state is extremely difficult to treat theoretically. This is due to the simultaneous appearance of quantum degeneracy, Coulomb correlations and thermal effects, as well as the overlap of plasma and condensed phases. Recent breakthroughs are due to the successful application of density functional theory (DFT) methods which, however, often lack the necessary accuracy and predictive capability for WDM applications. The situation has changed with the availability of the first ab initio data for the exchange-correlation free energy of the warm dense uniform electron gas (UEG) that were obtained by quantum Monte Carlo (QMC) simulations, for recent reviews, see Dornheim et al., Phys. Plasmas 24, 056303 (2017) and Phys. Rep. 744, 1-86 (2018). In the present article we review recent further progress in QMC simulations of the warm dense UEG: namely, ab initio results for the static local field correction G(q) and for the dynamic structure factor S(q, ω). These data are of key relevance for the comparison with x-ray scattering experiments at free electron laser facilities and for the improvement of theoretical models.In the second part of this paper we discuss simulations of WDM out of equilibrium. The theoretical approaches include Born-Oppenheimer molecular dynamics, quantum kinetic theory, timedependent DFT and hydrodynamics. Here we analyze strengths and limitations of these methods and argue that progress in WDM simulations will require a suitable combination of all methods. A particular role might be played by quantum hydrodynamics, and we concentrate on problems, recent progress, and possible improvements of this method.

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Section: A Summary Of Ab Initio Static Resultsmentioning

confidence: 99%

Ab initio simulation of warm dense matter

et al. 2020

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“…The uniform electron gas (UEG), often denoted as jellium or quantum one-component plasma, is one of the most important and fundamental model systems in physics and beyond [1,2]. For example, the UEG has facilitated key insights such as Fermi liquid theory [3], the quasi-particle picture of collective excitations [4], and the currently prevailing theory of superconductivity [5].…”

Section: Introductionmentioning

confidence: 99%

Strongly coupled electron liquid: Ab initio path integral Monte Carlo simulations and dielectric theories

et al. 2020

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The strongly coupled electron liquid provides a unique opportunity to study the complex interplay of strong coupling with quantum degeneracy effects and thermal excitations. To this end, we carry out extensive ab initio path integral Monte Carlo (PIMC) simulations to compute the static structure factor, interaction energy, density response function, and the corresponding static local field correction in the range of 20 ≤ rs ≤ 100 and 0.5 ≤ θ ≤ 4. We subsequently compare these data to several dielectric approximations, and find that different schemes are capable to reproduce different features of the PIMC results at certain parameters. Moreover, we provide a comprehensive data table of interaction energies and compare those to two recent parametrizations of the exchangecorrelation free energy, where they are available. Finally, we briefly touch upon the possibility of a charge-density wave. The present study is complementary to previous investigations of the uniform electron gas in the warm dense matter regime and, thus, further completes our current picture of this fundamental model system at finite temperature. All PIMC data are available online.

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“…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.…”

mentioning

confidence: 99%

“…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.…”

mentioning

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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The uniform electron gas

Cited by 145 publications

References 149 publications

Ab initio simulation of warm dense matter

Ab initio simulation of warm dense matter

Strongly coupled electron liquid: Ab initio path integral Monte Carlo simulations and dielectric theories

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

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