Ab initio path integral Monte Carlo approach to the static and dynamic density response of the uniform electron gas

Abstract

In a recent Letter [T. Dornheim et al., Phys. Rev. Lett. 121, 255001 (2018)] we have presented the first ab initio results for the dynamic structure factor S(q, ω) of the uniform electron gas for conditions ranging from the warm dense matter regime to the strongly correlated electron liquid. This was achieved on the basis of exact path integral Monte Carlo data by stochastically sampling the dynamic local field correction G(q, ω). In this paper, we introduce in detail this new reconstruction method and provide several practical demonstrations. Moreover, we thoroughly investigate the associated imaginary-time density-density correlation function F (q, τ ). The latter also gives us access to the static density-response function χ(q) and static local field correction G(q), which are compared to standard dielectric theories like the widespread random phase approximation. In addition, we study the high-frequency limit of G(q, ω) and provide extensive new results for the dynamic structure factor for different densities and temperatures. Finally, we discuss the implications of our findings for warm dense matter research and the interpretation of experiments.

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

“…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.…”

“…The latter would lead to large systematic deviations when χ(q) is small, which is potentially misleading, as one is typically interested in wave-number integrals over the density response, so that χ max is a more meaningful scale. Overall, we always find the largest deviations around the Fermi wave numbers, as it is expected [76,11,75], whereas they vanish in the limit of large wave numbers, where even RPA becomes exact. Furthermore, the relative size of the deviations is largest at low temperature where RPA (STLS) deviates from the PIMC data by a few percent (∼ 1%), but nearly vanishes for the largest depicted temperature, θ = 8, where we find ∆χ/χ max ∼ 0.1%.…”

“…">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.…”

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

“…In particular, the perturbation amplitude A must be sufficiently small such that all terms beyond a linear treatment in A can be neglected. Since detailed and accessible introductions to LRT have been presented elsewhere [2,3,18], here will only repeat the most important relations.…”

“…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]. In addition, it offers a plethora of remarkably rich physical effects, such as the emergence of a charge-density wave (CDW) [6][7][8] or spin-density wave [9], Wigner crystallization at low density [10][11][12][13][14], and an incipient excitonic mode [15][16][17][18].…”