Integral equation theory based dielectric scheme for strongly coupled electron liquids

Abstract

A novel dielectric scheme is proposed for strongly coupled electron liquids that handles quantum mechanical effects beyond the random phase approximation level and treats electronic correlations within the integral equation theory of classical liquids. The self-consistent scheme features a complicated dynamic local field correction functional and its formulation is guided by ab initio path integral Monte Carlo simulations. Remarkably, our scheme is capable to provide unprecedently accurate results for the static structure factor with the exception of the Wigner crystallization vicinity, despite the absence of adjustable or empirical parameters.

Effective electronic forces and potentials from ab initio path integral Monte Carlo simulations

“…We are convinced that our investigation will open up many avenues for important and impactful future research, and briefly sketch a number of promising possibilities: i) our PIMC results give one direct insight into the microscopic impact of nonlinear effects onto the effective interaction between a pair of electrons. This can be used as the basis for the further improvement of dielectric theories [123,126,143,144] and guide the development of explicitly nonlinear potentials [145,146]; ii) the possible role of the attractive minimum in F eff (r) as a pairing mechanism in the UEG, and its connection to the potential emergence of superconductivity in the electron liquid regime [92] deserve closer exploration; iii) our analysis has revealed the remarkably fast decay of fermionic exchange effects for r ∼ r s , which opens up the intriguing possibility for a further decomposition: use of fermionic PIMC for very small N to study short range exchange-correlation effects at r r s , use of Boltzmann PIMC to study diffraction at r s r 3r s , and use of dielectric theories for r r s to get a highly accurate description across the full domain of length scales. This might substantially increase the scope of feasible density-temperature combinations [85], and give us for the first time access to the regime of metallic densities at θ ∼ 0.1, .…”

“…This information concerning the competition between Coulomb correlations, quantum degeneracy, and diffraction effects can then be combined with other methods to model the large scale behaviour of the system. The combination of computational methods with theoretical models like dielectric theories [122][123][124][125][126] then allows for a highly accurate description of the system of interest everywhere [21, 23-25, 117, 118]. Likewise the fast decay of the effective force can be viewed as a theoretical justification for fragmentation methods [127] that partition the electron density into smaller subsystems [128].…”

The uniform electron gas at high temperatures: \emph{ab initio} path integral Monte Carlo simulations and analytical theory

“…Consequently, many approximate closure relations have been presented in the literature, most notably the schemes by Singwi, Tosi, Land, and Sjölander [11,14,15] (STLS), and by Vashista and Singwi (VS) [12,15,16]. Additional recent improvements include the hypernetted chain formulation by Tanaka [20] and the integral-equation based dielectric scheme by Tolias et al [21,22], which both constitute improvements over STLS at strong coupling.…”

“…Despite its apparent simplicity, the accurate description of the UEG had remained a most formidable challenge for decades, and facilitated a number of methodological innovations such as dielectric theories [11,12,13,14,15,16,17,18,19,20,21,22] and quantum-to-classical mappings [23,24,25,26]. The first rigorous results at T = 0 have been presented in the seminal work by Ceperley and Alder [27] on the basis of numerical quantum Monte Carlo (QMC) simulations.…”

“…This makes it possible to perform explicitly thermal DFT simulations [66] of WDM on the level of the local density approximation [67,68]. This has been followed by the rigorous investigation of a number of other properties of warm dense electrons, including the static density response [69,70,71,72,73,21,74,75], the momentum distribution function [76,77,78], and the static structure factor [79,73,58,59]. Moreover, it has even been possible to use path integral Monte Carlo (PIMC) [80,81,82] results for the imaginary-time version of the intermediate scattering function F (q, τ ) [cf.…”