<i>Ab initio</i>quantum Monte Carlo simulations of the uniform electron gas without fixed nodes: The unpolarized case

Dornheim, Tobias; Groth, Simon; Schoof, Tim; Hann, Connor T.; Bönitz, M.

doi:10.1103/physrevb.93.205134

Cited by 68 publications

(77 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These results are significant because restricted PIMC with free-particle nodes is often considered the most accurate method available to study real warm dense matter systems [9,34]. Our findings, when combined with the results of configuration and permutation-blocking PIMC simulations [35,[37][38][39], suggest that the free-particle nodal constraint may incur an error of 5%-10%, depending on the density and observable considered. We believe that exponentially scaling, systematically exact methods such as the i-DMQMC methods could be of use in analyzing and improving approximations made in restricted PIMC.…”

Section: 115701 (2016) P H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 58%

Accurate Exchange-Correlation Energies for the Warm Dense Electron Gas

et al. 2016

View full text Add to dashboard Cite

The density matrix quantum Monte Carlo (DMQMC) method is used to sample exact-on-average N-body density matrices for uniform electron gas systems of up to 10 124 matrix elements via a stochastic solution of the Bloch equation. The results of these calculations resolve a current debate over the accuracy of the data used to parametrize finite-temperature density functionals. Exchange-correlation energies calculated using the real-space restricted path-integral formalism and the k-space configuration pathintegral formalism disagree by up to ∼10% at certain reduced temperatures T=T F ≤ 0.5 and densities r s ≤ 1. Our calculations confirm the accuracy of the configuration path-integral Monte Carlo results available at high density and bridge the gap to lower densities, providing trustworthy data in the regime typical of planetary interiors and solids subject to laser irradiation. We demonstrate that the DMQMC method can calculate free energies directly and present exact free energies for T=T F ≥ 1 and r s ≤ 2. DOI: 10.1103/PhysRevLett.117.115701 The uniform electron gas is perhaps the most fundamental model in condensed matter physics. Core concepts such as Fermi liquid theory [1], quasiparticles and collective excitations [2,3], screening [4], the BCS theory of superconductivity [5], and Hohenberg-Kohn-Sham density-functional theory (DFT) [6,7], were all built on our understanding of the electron gas at low temperature. A growing interest in matter at extreme conditions, especially in the warm dense regime [8] found in inertial confinement fusion experiments [9], planetary interiors [10], and laser-irradiated solids [11], has sparked efforts to extend this understanding to much higher temperatures. Here, the electron gas also represents a useful model for hot lower density plasmas where electron-ion effects are less important [12]. This Letter concerns the properties of the electron gas at temperatures comparable to the Fermi energy.The quantitative successes of ground-state DFT rest on parametrizations of the correlation energy of the electron gas at zero temperature [13][14][15]. Errors of a few percent in the correlation functional have large effects on chemical bonding and phase diagrams, so these parametrizations are based on accurate quantum Monte Carlo (QMC) data [16]. Thermal DFT [17] treats thermal, quantum mechanical, many-body, and material effects explicitly and has emerged as a viable tool [18] for the study of warm dense matter, but requires as input a similarly accurate parametrization of the exchange-correlation free energy in the entire temperature-density plane [17,19,20]. A significant step towards providing these much needed data was recently made by Brown et al. [21] using the restricted path-integral Monte Carlo method, with local density parametrizations quickly following [22][23][24]. Soon after this, however, an alternative technique, configuration PIMC, was applied to the same problem and gave substantially different results [25,26].This Letter resolves the disagreement between the two p...

show abstract

Section: 115701 (2016) P H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 58%

Accurate Exchange-Correlation Energies for the Warm Dense Electron Gas

et al. 2016

View full text Add to dashboard Cite

show abstract

“…In particular, the widely used path integral Monte Carlo (PIMC) method [40,41,42] cannot access significant parts of the WDM regime, which sparked the need for new developments.This demand was met recently by a surge of new developments in the field of fermionic QMC simulations at finite temperature, e.g., Refs. [43,44,45,46,47,48,49,50,51,52]. On the one hand, Dornheim and co-workers [47,48,53] have introduced the so-called permutation blocking PIMC (PB-PIMC) method, which significantly alleviates…”

mentioning

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

View full text Add to dashboard Cite

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...

show abstract

“…The pioneering QMC simulations of the warm dense UEG by Brown et al [30] eliminated the sign problem by invoking the (uncontrolled) fixed-node approximation [31], but were nevertheless restricted to small systems of N = 33 (spin-polarized) and N = 66 (unpolarized) elecarXiv:1607.08076v2 [physics.plasm-ph] 9 Sep 2016 trons and to moderate densities, r s ≥ 1. Recently, we were able to show [32][33][34] that accurate simulations of these systems are possible over a broad parameter range without any nodal restriction. Our approach combines two independent methods, configuration path-integral Monte Carlo (CPIMC) [35][36][37] and permutation blocking PIMC [38,39], which allow for accurate simulations at high (r s 1) and moderate densities (r s 1 and θ 0.5), respectively.…”

mentioning

confidence: 99%

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

et al. 2016

View full text Add to dashboard Cite

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...

show abstract

Ab initioquantum Monte Carlo simulations of the uniform electron gas without fixed nodes: The unpolarized case

Cited by 68 publications

References 56 publications

Accurate Exchange-Correlation Energies for the Warm Dense Electron Gas

Accurate Exchange-Correlation Energies for the Warm Dense Electron Gas

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

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

Contact Info

Product

Resources

About