For the ground state of the homogeneous electron gas (jellium), it is shown how the cumulant decomposition of the 2-matrix leads to the cumulant decomposition of the structure factors Sa,p(q) for the antiparallel (a) and parallel (p) spin pairs and how it simultaneously allows one to derive the momentum distribution n(k), which is a one-body quantity [Phys. Rev. A 86, 012508 (2012)]. The small-q and large-q behavior of Sa,p(q), and their normalizations are derived and compared with the results of P. Gori-Giorgi et al. [Physica A 280, 199 (2000) and Phys. Rev. B 61, 7353 (2000)].
For the first time, the cumulant 2-body reduced density matrix (= 2-matrix) of the spin-unpolarized homogeneous electron gas (HEG) is considered. This
γc 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
γc 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
γc - through a certain contraction procedure, cf Eqs.(2.25)-(2.28). In particular, this
γc 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.
It is shown how the normalization sum rules of the spin-parallel and spin-antiparallel (or equivalently singlet and triplet) pair densities of the homogeneous electron gas can be rewritten equivalently as sum rules for the scattering phase shifts of those two-body wave functions (geminals), with which the pair densities have been parametrized recently. These sum rules relate two-body quantities to a one-body quantity: namely, the asymptotics of the pair-density geminals to the momentum distribution.
Abstract The cumulant 2‐matrix χ is that part of the two‐body reduced density matrix γ2, which cannot be reduced to products of the one‐body reduced density matrix (1‐matrix) γ. This irreducible part χ is calculated perturbatively for the high‐density electron gas (EG) in its ground state, such that the pair densities and the interaction energy are correctly reproduced in their high‐density limits, which are exactly known and summarized here. From the thus available cumulant 2‐matrix the pair density in momentum space can be derived and used for a fluctuation analysis and compared with the analog analysis in position space, where it is concluded that “correlation suppresses fluctuations”. The perturbatively available cumulant 2‐matrix χ can be used also for the high‐density electron gas to start the iterative solution of the Yasuda integral equation of density matrix functional theory (DMFT), which is a nonlinear functional relation between the cumulant 2‐matrix χ and the 1‐matrix γ recently derived from the contracted Schrödinger equation approach: χY[γ]. From the perturbatively determined χ one can find another functional χ[γ] as an alternative approximation for a DMFT. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002
The random phase approximation (RPA) provides a qualitatively good approximation of electronic correlation in many systems. It has been successfully applied to the spin-unpolarized homogeneous electron gas (HEG) for decades, especially in the studies of its many properties such as correlation energy, momentum distribution and the spin resolved pair correlation function and structure factor. However, the RPA neglects important contributions to the spin-parallel structure factor originating from exchange effects. We derive an approximation for the spin-parallel structure factor including the lowest order exchange process beyond the RPA analytically by means of contour integration and evaluate it numerically by means of a Monte-Carlo integration. A generalized Hellmann-Feynman theorem with functional derivatives is used.
We present a calculation of the spin-averaged and spin-resolved pair distribution functions for a homogeneous gas of electrons moving in a plane with e2/r interactions at coupling strength rs = 10. The calculation is based on the solution of a two-electron scattering problem for both parallelspin- and antiparallel-spin-pairs interacting via effective spin-dependent many-body potentials. The scattering potentials are modeled within the approach proposed by Kukkonen and Overhauser to treat exchange and correlations under close constraints imposed by sum rules. We find very good agreement with quantum MonteCarlo data for the spin-averaged pair density. We also find that short-range pairing between parallel-spin electrons is beginning to emerge in the paramagnetic fluid at this coupling strength, as a precursor of a transition to a fully spin-polarized fluid state occurring at stronger coupling.