The on-shell self-energy of the uniform electron gas in its weak-correlation limit

Abstract

The ring-diagram partial summation (or RPA) for the ground-state energy of the uniform electron gas (with the density parameter $r_s$) in its weak-correlation limit $r_s\to 0$ is revisited. It is studied, which treatment of the self-energy $\Sigma (k,\omega )$ is in agreement with the Hugenholtz-van Hove (Luttinger-Ward) theorem $\mu -{\mu }_0=\Sigma (k_{\mathrm{F}},\mu )$ and which is not. The correlation part of the lhs h as the RPA asymptotics $a\ln r_s+a^{\prime }+O(r_s)$ [in atomic units]. The use of renormalized RPA diagrams for the rhs yields the similar expression $a\ln r_s+a^{\prime \prime }+O(r_s)$ with the sum rule $a^{\prime }=a^{\prime \prime }$ resulting from three sum rules for the components of $a^{\prime }$ and $a^{\prime \prime }$. This includes in the second order of exchange the sum rule ${\mu }_{2\mathrm{x}}={\Sigma }_{2\mathrm{x}}$ [P. Ziesche, Ann. Phys. (Leipzig), 2006].

19 pages, 10 figures

References in corpus (5)

• New measure of electron correlation
• Multiple electron-hole scattering effect on quasiparticle properties in a homogeneous electron gas
• The self-energy of the uniform electron gas in the second order of exchange
• Analysis of the second order exchange self energy of a dense electron gas
• On the (anisotropic) uniform metallic ground states of fermions interacting through arbitrary two-body potentials in d dimensions

Cited by in corpus (2)

• The high-density electron gas: How its momentum distribution n(k) and its static structure factor S(q) are mutually related through the off-shell self-energy Sigma(k,omega)
• Self-consistent Spectral Function for Non-Degenerate Coulomb Systems and Analytic Scaling Behaviour