Self-consistent Spectral Function for Non-Degenerate Coulomb Systems and Analytic Scaling Behaviour

TL;DR

This paper presents a self-consistent spectral function analysis for non-degenerate Coulomb systems using the GW^0 method, revealing collective plasma effects and an analytic scaling law for the self-energy at low densities.

Contribution

It introduces a novel analytic scaling law for the self-energy in Coulomb systems and applies the GW^0 method for improved correlation effects beyond quasi-particles.

Findings

Spectral functions show plasma mode behavior at small wavenumbers.

Self-energy follows a power-law Im Sigma ~ -n^(1/4) at low densities.

Results resolve issues with the quasi-particle approximation at vanishing density.

Abstract

Novel results for the self-consistent single-particle spectral function and self-energy are presented for non-degenerate one-component Coulomb systems at various densities and temperatures. The GW^0-method for the dynamical self-energy is used to include many-particle correlations beyond the quasi-particle approximation. The self-energy is analysed over a broad range of densities and temperatures (n=10^17/cm^3-10^27/cm^3, T=10^2 eV/k_B-10^4 eV/k_B). The spectral function shows a systematic behaviour, which is determined by collective plasma modes at small wavenumbers and converges towards a quasi-particle resonance at higher wavenumbers. In the low density limit, the numerical results comply with an analytic scaling law that is presented for the first time. It predicts a power-law behaviour of the imaginary part of the self-energy, Im Sigma ~ -n^(1/4). This resolves a long time problem of the quasi-particle approximation which yields a finite self-energy at vanishing density.