Abstract
The correlation energy of the homogeneous electron gas is evaluated by solving the Bethe-Salpeter equation (BSE) beyond the Tamm-Dancoff approximation for the electronic polarisation propagator. The BSE is expected to improve upon the random phase approximation, owing to the inclusion of exchange diagrams. For instance, since the BSE reduces in second order to M{\o}ller-Plesset perturbation theory, it is self-interaction free in second order. Results for the correlatione energy are compared with Quantum Monte Carlo benchmarks and excellent agreement is observed. For low densities, however, we find imaginary eigenmodes in the polarisation propagator. To avoid the occurence of imaginary eigenmodes, an approximation to the BSE kernel is proposed, which allows to completely remove this issue in the low electron density region. We refer to this approximation as the random phase approximation with screened exchange (RPAsX). We show that this approximation even slightly improves upon the standard BSE kernel.
Highlights
The study of the homogeneous electron gas (HEG) as a model in condensed matter theory, has a long tradition
It allows one to focus on the properties of the manyelectron system without complications arising from discretized lattice symmetry
The impact of the basis-set incompleteness is shown in Fig. 2: for the set of densities considered, a linear convergence behavior with the inverse of the number of bands is observed [14]
Summary
The study of the homogeneous electron gas (HEG) as a model in condensed matter theory, has a long tradition. The field factor can be related to the irreducible electronhole scattering amplitude This appears in the integral (and recursive) equation for the polarization propagator, known as the Bethe-Salpeter equation (BSE). We implement a computational scheme to solve the BSE when its kernel is derived from the GW0 approximation for the self-energy. The BSE has been exploited to describe hydrogen dissociation [32], to gain access to optical properties of semiconductors and insulators [33,34,35], and to study excitonic effects in extended [36] and molecular systems [37,38]. The fluctuation-dissipation theorem is exploited to relate the ground-state correlation energy to the system’s linear response functions integrated over the AC path. IV, the computational scheme proposed and related approximations are put to fruition to assess the correlation energy of the HEG
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