Anomalous propagators and the particle-particle channel: Hedin's equations

Abstract

Hedin's equations provide an elegant route to compute the exact one-body Green's function (or propagator) via the self-consistent iteration of a set of non-linear equations. Its first-order approximation, known as $GW$, corresponds to a resummation of ring diagrams and has shown to be extremely successful in physics and chemistry. Systematic improvement is possible, although challenging, via the introduction of vertex corrections. Considering anomalous propagators and an external pairing potential, we derive a new self-consistent set of closed equations equivalent to the famous Hedin equations but having as a first-order approximation the particle-particle (pp) $T$-matrix approximation where one performs a resummation of the ladder diagrams. This pp version of Hedin's equations offers a way to go systematically beyond the $T$-matrix approximation by accounting for low-order pp vertex corrections.

12 pages, 5 figures (Supp. Mat. available)

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Cited by in corpus (11)

• Beyond quasi-particle self-consistent $GW$ for molecules with vertex corrections
• Anomalous propagators and the particle-particle channel: Bethe-Salpeter equation
• Double Ionization Potential Equation-of-Motion Coupled-Cluster Approach with Full Inclusion of 4-Hole-2-Particle Excitations and Three-Body Clusters
• Accurate and Efficient Prediction of Double Excitation Energies Using the Particle-Particle Random Phase Approximation
• Fully Analytic Nuclear Gradients for the Bethe--Salpeter Equation
• Joint Approximate Diagonalization approach to Quasiparticle Self-Consistent $GW$ calculations
• Analytic $G_0{W}_0$ gradients based on a double-similarity transformation equation-of-motion coupled-cluster treatment
• Complex Absorbing Potential Green's Function Methods for Resonances
• Parquet theory for molecular systems: Formalism and static kernel parquet approximation
• Gor'kov-Hedin-Baym Equations for Quantum Many-Body Systems with Spin-Dependent Interactions
• LibppRPA: An Open-Source Library for Particle-Particle Random Phase Approximation