Strongly coupled electron liquid: 
<i>Ab initio</i>
 path integral Monte Carlo simulations and dielectric theories

Dornheim, Tobias; Sjostrom, Travis; Tanaka, Shigenori; Vorberger, Jan

doi:10.1103/physrevb.101.045129

Cited by 65 publications

(102 citation statements)

References 106 publications

(203 reference statements)

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“…In the HED regime, both dielectric methods provide accurate results with a maximum deviation in χ(q) of ∼ 4% (∼ 1%) for RPA (STLS) at θ = 0.85 and r s = 0.5. In this way, we have bridged the gap between previous PIMC simulation results in the WDM regime and beyond [75,11,76] and perturbative expansions like dielectric theories [3,130,131]; iii) we have shown that our PIMC approach to the static density response converges towards RPA both for high temperatures and densities, and is in striking agreement to highly accurate CPIMC data, where they are available. This illustrates the consistency of our approach, and further corroborates our current understanding of the UEG at finite temperature.…”

Section: Discussionsupporting

confidence: 73%

“…Shortly thereafter, two of us [76] have extended these efforts to even stronger coupling strength, 20 ≤ r s ≤ 100 (blue diamonds), where the UEG forms an electron Figure 1. Parameter overview of quantum Monte Carlo data for the static density response of the uniform electron gas in the r s -θ plane.…”

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confidence: 99%

“…The blue diamonds correspond to the strongly coupled electron liquid (EL) studied in Ref. [76]. The purple triangles depict our new simulation data for the high-energy-density (HED) regime, with the upward arrows indicating PIMC results for θ = 8 that is available at r s = 0.05, 0.1, 0.3, and 0.5.…”

mentioning

confidence: 99%

“…This further illustrates the consistency of our PIMC approach to the static density response and corroborates the high quality of the results presented in Refs. [75,76,11].…”

mentioning

confidence: 99%

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Ab initio path integral monte carlo simulation of the uniform electron gas in the high energy density regime

Dornheim

Moldabekov

Vorberger

et al. 2020

Plasma Phys. Control. Fusion

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The response of the uniform electron gas (UEG) to an external perturbation is of paramount importance for many applications. Recently, highly accurate results for the static density response function and the corresponding local field correction have been provided both for warm dense matter [J. Chem. Phys. 151, 194104 (2019)] and strongly coupled electron liquid [Phys. Rev. B 101, 045129 (2020)] conditions based on exact ab initio path integral Monte Carlo (PIMC) simulations. In the present work, we further complete our current description of the UEG by exploring the high energy density regime, which is relevant for, e.g., astrophysical applications and inertial confinement fusion experiments. To this end, we present extensive new PIMC results for the static density response in the range of 0.05 ≤ r s ≤ 0.5 and 0.85 ≤ θ ≤ 8. These data are subsequently used to benchmark the accuracy of the widely used random phase approximation and the dielectric theory by Singwi, Tosi, Land, and Sjölander (STLS). Moreover, we compare our results to configuration PIMC data where they are available and find perfect agreement with a relative accuracy of 0.001 − 0.01%. All PIMC data are available online.The Uniform Electron Gas in the High Density Regime 2 IntroductionThe uniform electron gas (UEG), also known as jellium or quantum one-component plasma, is defined as a system of Coulomb interacting electrons in a neutralizing homogeneous background and constitutes one of the most import model systems in physics and chemistry [1,2,3]. Having been introduced as a simple model description for conduction electrons in metals [4], the UEG exhibits a variety of interesting effects, such as Wigner crystallization [5,6,7] and a possible incipient excitonic mode which has been predicted to appear at low density [8,9,10,11].Moreover, the availability of highly accurate quantum Monte Carlo (QMC) data [12,13,14,15,16] at metallic densities and zero-temperature has sparked remarkable developments in many fields, most notably the hitherto unequaled success of density functional theory (DFT) regarding the description of real materials [17,18].Recently, the interest in matter under extreme conditions [19] has led to the need for analogous quantum Monte Carlo data at finite temperature. Of particular importance is the so-called warm dense matter (WDM) regime, which is defined by two characteristic parameters that are both of the order of one: i) the density parameter r s = r/a B (with r and a B being the average inter-particle distance and first Bohr radius) and ii) the reduced temperature θ = k B T /E F (with k B and E F being the Boltzmann constant and Fermi energy [1]), cf. Fig. 1 below. These conditions occur in astrophysical objects like giant planet interiors [20,21,22] and are expected to manifest on the pathway towards inertial confinement fusion [23]. Furthermore, WDM is nowadays routinely realized in large research facilities around the globe like the Linac Coherent Light Source (LCLS) [24], the National Ignition Facility (NIF) [25], and th...

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Section: Discussionsupporting

confidence: 73%

mentioning

confidence: 99%

mentioning

confidence: 99%

“…This further illustrates the consistency of our PIMC approach to the static density response and corroborates the high quality of the results presented in Refs. [75,76,11].…”

mentioning

confidence: 99%

See 2 more Smart Citations

Ab initio path integral monte carlo simulation of the uniform electron gas in the high energy density regime

Dornheim

Moldabekov

Vorberger

et al. 2020

Plasma Phys. Control. Fusion

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“…Therefore, addressing this issue would require a modification of the corresponding Padé approximation to automatically fulfill some additional constraints. ii) the current validity domain of, e.g., the GDSMFBB parametrization to 0 ≤ r s ≤ 20 can be significantly extended by incorporating the recent ab initio PIMC results for the electron liquid regime (20 ≤ r s ≤ 100) by Dornheim et al [128]. iii) new ab intio QMC results at low temperature, θ ∼ 10 −1 , could help to more accurately resolve open thermodynamic questions like the effective mass enhancement [129], but are difficult to obtain due to the notorious fermion sign problem [130].…”

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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Nonlinear interaction of external perturbations in warm dense matter

Dornheim

Vorberger

Moldabekov

et al. 2022

Contributions to Plasma Physics

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We present extensive new ab initio path integral Monte Carlo (PIMC) results for an electron gas at warm dense matter conditions that is subject to multiple harmonic perturbations. In addition to the previously investigated nonlinear effects at the original wave number (Dornheim et al., Phys. Rev. Lett., 2020, 125, 085001) and the excitation of higher harmonics (Dornheim et al., Phys. Rev. Res., 2021, 3, 033231), the presence of multiple external potentials leads to mode-coupling effects, which constitute the dominant nonlinear effect and lead to a substantially more complicated density response compared to linear response theory. One possibility to estimate mode-coupling effects from a PIMC simulation of the unperturbed system is given in terms of generalized imaginary-time correlation functions that have been recently introduced by Dornheim et al. (J. Chem. Phys., 2021, 155, 054110). In addition, we extend our previous analytical theory of the nonlinear density response of the electron gas in terms of the static local field correction (Dornheim et al., 2020, Phys. Rev. Lett., 125, 235001), which allows for a highly accurate description of the PIMC results with negligible computational cost.

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

Cited by 65 publications

References 106 publications

Ab initio path integral monte carlo simulation of the uniform electron gas in the high energy density regime

Ab initio path integral monte carlo simulation of the uniform electron gas in the high energy density regime

Ab initio simulation of warm dense matter

Nonlinear interaction of external perturbations in warm dense matter

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