Optimized correlations inspired by perturbation theory

Panholzer, Martin; Hobbiger, Raphael; Böhm, Helga M.

doi:10.1103/physrevb.99.195156

Cited by 6 publications

(11 citation statements)

References 56 publications

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“…Moreover, the investigation both of the density response function χ(q) and G(q) itself are interesting in their own right, and we find a pronounced dependence of the LFC on density and temperature, with a nontrivial behaviour around intermediate q-values and a negative large-q tail for certain parameters. Furthermore, our results can be used to comprehensively gauge the accuracy of widely used approximations like dielectric theory [100][101][102]111] and to benchmark and guide the developments of new methods [112]. Finally, we expect the presented combination of computationally expensive ab initio calculations with modern machine-learning methods to be a promising strategy for many applications in many-body physics and beyond.…”

Section: Arxiv:190708473v1 [Physicsplasm-ph] 19 Jul 2019mentioning

confidence: 87%

The static local field correction of the warm dense electron gas: An ab initio path integral Monte Carlo study and machine learning representation

Dornheim

Vorberger

Groth

et al. 2019

The Journal of Chemical Physics

100

206

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The study of matter at extreme densities and temperatures as they occur in astrophysical objects and state-of-the art experiments with high-intensity lasers is of high current interest for many applications. While no overarching theory for this regime exists, accurate data for the density response of correlated electrons to an external perturbation are of paramount importance. In this context, the key quantity is given by the local field correction (LFC), which provides a wave-vector resolved description of exchange-correlation effects. In this work, we present extensive new path integral Monte Carlo (PIMC) results for the static LFC of the uniform electron gas, which are subsequently used to train a fully connected deep neural network. This allows us to present a continuous representation of the LFC with respect to wave-vector, density, and temperature covering the entire warm dense matter regime. Both the PIMC data and neural-net results are available online. Moreover, we expect the presented combination of ab initio calculations with machinelearning methods to be a promising strategy for many applications.

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Section: Arxiv:190708473v1 [Physicsplasm-ph] 19 Jul 2019mentioning

confidence: 87%

The static local field correction of the warm dense electron gas: An ab initio path integral Monte Carlo study and machine learning representation

Dornheim

Vorberger

Groth

et al. 2019

The Journal of Chemical Physics

100

206

View full text Add to dashboard Cite

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“…Let us briefly summarize our key results as follows: i) we provide highly accurate benchmark data both for χ(q) and G(q) for 24 density-temperature combinations in the range of 0.85 ≤ θ ≤ 8 and 0.05 ≤ r s ≤ 0.5. These data are available online [127] and can be used to benchmark new many-body approximations [80,128,129]; ii) we have compared the new results against both RPA and STLS. 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.…”

Section: Discussionmentioning

confidence: 99%

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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“…Unlike the bosonic systems, a truly FHNC formulation for the effective interaction in Fermi gases leads to a very complicated set of coupled equations [45]. However, several simplified recipes have tried to implement the exact weak or strong-coupling limiting behavior in the effective interaction and proved to give reasonably accurate results in the corresponding limits [46,47]. In this work, we follow the recipe of Kallio and Piilo (KP), which has been tailored to exactly capture the Fermi statistics and weak-coupling behavior [46].…”

Section: A Fermi-hypernetted-chain Euler-lagrange Approximationmentioning

confidence: 99%

“…Recently, Panholzer, Hobbiger, and Böhm (PHB) proposed a new particle-hole effective potential for the Fermihypernetted-chain approximation, based on the approximate summation of ladder and ring diagrams [47]. The selfconsistent equations of PHB essentially become identical to the KP equations if one replaces the Fermi potential w F (r) in equation ( 5) with…”

Section: Appendix B: Comparison Between Kallio-piilo and Ladder+appro...mentioning

confidence: 99%

Rydberg-dressed Fermi liquid: Correlations and signatures of droplet crystallization

et al. 2021

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We investigate the effects of many-body correlations on the ground-state properties of a single-component ultracold Rydberg-dressed Fermi liquid with purely repulsive interparticle interactions in both three and two spatial dimensions. We employed the Fermi-hypernetted-chain Euler-Lagrange approximation and observed that the contribution of the correlation energy on the ground-state energy becomes significant at intermediate values of the soft-core radius and large coupling strengths. For small and large soft-core radii, the correlation energy is negligible and the ground-state energy approaches the Hartree-Fock value. The positions of the main peaks in static structure factor and pair distribution function in the homogeneous fluid phase signal the formation of quantum droplet crystals with several particles confined inside each droplet.

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Optimized correlations inspired by perturbation theory

Cited by 6 publications

References 56 publications

The static local field correction of the warm dense electron gas: An ab initio path integral Monte Carlo study and machine learning representation

The static local field correction of the warm dense electron gas: An ab initio path integral Monte Carlo study and machine learning representation

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

Rydberg-dressed Fermi liquid: Correlations and signatures of droplet crystallization

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