Reduced density matrices, their spectral resolutions, and the Kimball-Overhauser approach

TL;DR

This paper explores the spectral properties of reduced density matrices in the homogeneous electron gas, introduces new sum rules for scattering phase shifts, and connects these to the Kimball-Overhauser approach using cumulants.

Contribution

It derives new sum rules for scattering phase shifts related to pair densities and extends the Kimball-Overhauser approach with spectral and contraction properties of reduced density matrices.

Findings

New sum rules for phase shifts and pair density normalization

Connection between reduced density matrices and the Kimball-Overhauser approach

Analysis of cumulants and their size-extensivity in the thermodynamic limit

Abstract

Recently, it has been shown, that the pair density of the homogeneous electron gas can be parametrized in terms of 2-body wave functions (geminals), which are scattering solutions of an effective 2-body Schr\"odinger equation. For the corresponding scattering phase shifts, new sum rules are reported in this paper. These sum rules describe not only the normalization of the pair density (similar to the Friedel sum rule of solid state theory), but also the contraction of the 2-body reduced density matrix. This allows one to calculate also the momentum distribution, provided that the geminals are known from an appropriate screening of the Coulomb repulsion. An analysis is presented leading from the definitions and (contraction and spectral) properties of reduced density matrices to the Kimball-Overhauser approach and its generalizations. Thereby cumulants are used. Their size-extensivity is related to the thermodynamic limit.