Thermodynamics of the uniform electron gas: Fermionic path integral Monte Carlo simulations in the restricted grand canonical ensemble

Abstract

The uniform electron gas (UEG) is one of the key models for the understanding of warm dense matter—an exotic, highly compressed state of matter between solid and plasma phases. The difficulty in modelling the UEG arises from the need to simultaneously account for Coulomb correlations, quantum effects, and exchange effects, as well as finite temperature. The most accurate results so far were obtained from quantum Monte Carlo (QMC) simulations with a variety of representations. However, QMC for electrons is hampered by the fermion sign problem. Here, we present results from a novel fermionic propagator path integral Monte Carlo in the restricted grand canonical ensemble. The ab initio simulation results for the spin‐resolved pair distribution functions and static structure factor are reported for two isotherms θ=1,2 (T in the units of the Fermi temperature). Furthermore, we combine the results from the linear response theory in the Singwi‐Tosi‐Land‐Sjölander scheme with the QMC data to remove finite‐size errors in the interaction energy. We present a new corrected parametrization for the interaction energy vfalse(rs,θfalse) and the exchange–correlation free energy fnormalxcfalse(rs,θfalse) in the thermodynamic limit, and benchmark our results against the restricted path integral Monte Carlo by Brown et al. [Phys. Rev. Lett. 110, 146405 (2013)] and configuration path integral Monte Carlo/permutation‐blocking path integral Monte Carlo by Dornheim et al. [Phys. Rev. Lett. 117, 115701 (2016)].

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

“…surprisingly large bias has subsequently been substantiated in independent studies [17,[76][77][78]. This unsatisfactory situation has sparked a recent surge of activity regarding the development of fermionic QMC methods at finite temperature [76,77,[79][80][81][82][83][84][85][86][87]; see Ref. [78] for a topical discussion of some of these developments.…”

Dynamic properties and the roton mode attenuation in the liquid 3He: an ab initio study within the self-consistent method of moments

“…( 1). This model ISF is compared to the physical one obtained in our PIMC simulations [17] using the sampled particle trajectories {r 1 (τ ), r 2 (τ ), . .…”

“…First, we introduce the two-parameter Shannon entropy functional defined by the spectral density function (17) where ω = {ω 1 , ω 2 , ω 3 , ω 4 }, and resolve the corresponding maximization problem with respect to ω 3(4) (q), with ω 1(2) (q) being fixed by the known sum rules. To solve the extremum conditions for two unknown frequencies…”

“…QMC methods are not restricted to a low-coupling limit and include, from the first principles, the exchange-correlation contributions to the thermodynamic observables. Moreover, the ensemble averages (population of excited states) can be accounted for very efficiently via the sampling of the statistical density matrix implemented by the path integral Monte Carlo (PIMC) method [6,[15][16][17].…”

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

“…Evidently, previous ground-state results for the UEG are insufficient for an accurate theoretical description of these extreme states, which has sparked a series of new developments in the field of fermionic QMC simulations of the UEG in the WDM regime [52,53,54,55,56,57,58,59,60,61,62]. These efforts have culminated in the first accurate parametrizations of the XC free energy f xc (r s , θ, ξ σ ) [with ξ σ = (N ↑ − N ↓ )/N being the spin-polarization] of the UEG [2,63,64,65].…”