Ab initio path-integral Monte Carlo results for the one-particle spectral function of the warm dense electron gas

TL;DR

This work provides quasi-exact, ab initio path-integral Monte Carlo results for the Matsubara Green's function of the warm dense uniform electron gas across $r_s=1$ to $10$, enabling approximation-free determinations of the static self-energy $\Sigma_\infty(p)$ and the one-particle spectral function $A(p,\omega)$. By reconstructing $A(p,\omega)$ from $G(p,\tau)$ with a differential-evolution analytic-continuation approach and comparing to $G_0W_0$ and cumulant-based models, the authors show that dynamic screening captured by GW significantly overestimates damping and fails to reproduce spectral shape, while the static Fock shift provides the main low-momentum energy reduction and no distinct satellites appear at the studied temperatures. The results offer robust benchmarks for improved many-body theories, and the methodology extends to real two-component warm dense matter, where it can inform interpretations of X-ray spectroscopy, DOS calculations, and band-gap corrections beyond static exchange kernels. Overall, the work establishes a principled first-principles route to connect imaginary-time correlation data with real-frequency spectra in WDM, with broad implications for theory, simulation, and experiment.

Abstract

We compute quasi-exact \emph{ab initio} path-integral Monte Carlo results for the Matsubara Green's function of the uniform electron gas (UEG) at finite temperature over a broad range of coupling strengths ($r_s=1,\dots,10)$. This allows us to present approximation-free results for the static self-energy $Σ_\infty(p)$ and spectral function $A(p,ω)$, and to benchmark previous approximate results for the UEG. In addition, our work opens up intriguing avenues to study the single-particle spectrum and density of states of real warm dense matter systems based on truly first principles.

Figures (7)

• Figure 1: Imaginary-time Green's function at $\theta\approx 2$, $r_s\approx 10$, unpolarized, $\langle N\rangle \approx 20$. Finite-size effects are negligible at these conditions, which agrees with previous investigations of other $p$-resolved properties dornheim_prlDornheim_PRE_2020, see also the Supplemental Material supplement.
• Figure 2: First moment of the spectral function for five densities and the same parameters as in Fig. \ref{['fig:A_rs']}. Self-consistent Fock calculations (dotted lines) are compared to PIMC results (colored symbols) that have been obtained directly from the MGF following the procedure from Ref. Dornheim_moments2023, see the Supplemental Material for additional details supplement.
• Figure 3: Spectral function at $r_s=4, \langle N\rangle \approx 20$ and $\theta=2$ (unpolarized) for different momenta $p$. The ideal quasi-particle dispersion, $\epsilon_p = p^2/2 - \mu_0$, and one-shot Fock results (direct evaluation of Eq. \ref{['eq:sigma_fock']} using the ideal $n(p)$ and $\mu_0$) are shown by the dotted and dashed black curves, respectively. The dashed magenta and dash-dotted blue curves correspond to the cumulant expansion from Ref. Kas2017 and $G_0 W_0$. Insets demonstrate the effect of varying the degeneracy parameter $\theta$, for two momenta.
• Figure 4: Spectral function of the fully polarized UEG for $p=0$, $\theta=2$ and 5 different coupling parameters $r_s$, $\langle N\rangle \approx 10$. The dotted lines indicate the quasi-particle position predicted by self-consistent Fock calculations.
• Figure 5: PIMC configurations involving only closed trajectories (left panel) and a worm (right panel).