Dynamically screened vertex correction to $GW$

Abstract

Diagrammatic perturbation theory is a powerful tool for the investigation of interacting many-body systems, the self-energy operator $\Sigma$ encoding all the variety of scattering processes. In the simplest scenario of correlated electrons described by the $GW$ approximation for the electron self-energy, a particle transfers a part of its energy to neutral excitations. Higher-order (in screened Coulomb interaction $W$) self-energy diagrams lead to improved electron spectral functions (SF) by taking more complicated scattering channels into account and by adding corrections to lower order self-energy terms. However, they also may lead to unphysical negative spectral function. The resolution of this difficulty has been demonstrated in our previous works. The main idea is to represent the self-energy operator in a Fermi Golden rule form which leads to the manifestly positive definite SF and allows for a very efficient numerical algorithm. So far, the method has only been applied to 3D electron gas, which is a paradigmatic system, but a rather simple one. Here, we systematically extend the method to 2D including realistic systems such as mono and bilayer graphene. We focus on one of the most important vertex function effects involving the exchange of two particles in the final state. We demonstrate that it should be evaluated with the proper screening and discuss its influence on the quasiparticle properties.

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• Time-linear scaling NEGF methods for real-time simulations of interacting electrons and bosons. I. Formalism
• Exploring the Statically Screened $G3W2$ Correction to the $GW$ Self-Energy: Charged Excitations and Total Energies of Finite Systems
• Comparing self-consistent GW and vertex corrected G0W0 (G0W0Γ) accuracy for molecular ionization potentials
• Solving the Bethe-Salpeter equation with exponential convergence
• Two-component $GW$ calculations: Cubic scaling implementation and comparison of vertex corrected and partially self-consistent $GW$ variants
• The three channels of many-body perturbation theory: $GW$, particle-particle, and electron-hole $T$-matrix self-energies
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• First-principles modelling for time-resolved ARPES under different pump-probe conditions
• Electronic structure of van der Waals ferromagnet CrI${}_3$ from self consistent vertex corrected GW approaches
• A unified Green's function approach for spectral and thermodynamic properties from algorithmic inversion of dynamical potentials
• Embedding vertex corrections in GW self-energy: theory, implementation, and outlook
• Cutting rules and positivity in finite temperature many-body theory