New approach to the one-particle Green's function for finite Fermi systems

A new approach to the one-particle Green's functions $\mathit{G}$ for finite electronic systems is presented. This approach is based on the diagrammatic perturbation expansions of the Green's function and of the dynamic self-energy part $\mathit{M}$ related to $\mathit{G}$ via the Dyson equation. The exact summation of the latter expansion is reformulated in terms of a simple algebraic form referred to as algebraic diagrammatic construction (ADC). The ADC defines in a systematical way a set of approximation schemes ($n\mathrm{th}$-order ADC schemes) that represent infinite partial summations for $\mathit{M}$ and (via the Dyson equation) for $\mathit{G}$ being complete through $n\mathrm{th}$ order of perturbation theory. The corresponding mathematical procedures are essentially Hermitian eigenvalue problems in restricted configuration spaces of unperturbed ionic configurations. Explicit equations for the second-, third-, and fourth-order ADC schemes are derived and analyzed. While the second- and third-order schemes can be viewed as systematic rederivations of previous approximation schemes, the fourth-order ADC scheme represents a complete fourth-order approximation for the self-energy and the one-particle Green's function which was hitherto not available.