2011/08/09 by P. Ziesche, Ziesche, P.
Chemistry · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced Physical and Chemical Molecular Interactions #Atomic and Molecular Physics #FOS: Physical sciences #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.1108.1912
openalex publication_date 2011/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For the first time, the cumulant 2-body reduced density matrix (= 2-matrix) of the spin-unpolarized homogeneous electron gas (HEG) is considered. This γ\rm c proves to be the common source for both the momentum distribution n(k) and the static structure factor S(q). Within many-body perturbation theory, this γ\rm c is given by only \it linked diagrams (with 2 open particle-hole lines as well as with closed loops and interaction lines). Here it is worked out in detail, how the 1-body quantity n(k) follows from the 2-body quantity γ\rm c - through a certain contraction procedure, cf Eqs.(2.25)-(2.28). In particular, this γ\rm c is developed for the high-density HEG. Its correctness is checked by deriving from it n(k) and S(q), known from the random-phase approximation (RPA). This study opens the way to a more sophisticated HEG description in terms of cumulant geminals or/and variational methods. Besides, the cumulant structure factor (CSF) of the exchange in lowest order is explicitly given and sum rules for the CSFs and their small- and large-q behavior (beyond RPA) are systematically summarized within the plasmon sum rule, coalescing theorems, and the inflexion-point trajectory.