Electron gas beyond the random-phase approximation: Algebraic screening

Using the standard many-body perturbation theory at finite temperature, we exhibit diagrams, not included in the usual random-phase-approximation ring summation, that lead to a 1/‖x ${\mathrm{\Vert }}^{10}$ decay of the charge-charge correlation. The quantum origin of this absence of exponential screening is clearly displayed in a semiclassical representation of the electron gas by functional integration, where the effective potential obtained by chain summation is of the dipolar type.