Related papers: Beyond the GW approximation: combining correlation…
We derive the explicit expression of the three self-energies that one encounters in many-body perturbation theory: the well-known $GW$ self-energy, as well as the particle-particle and electron-hole $T$-matrix self-energies. Each of these…
With the aim of identifying universal trends, we compare fully self-consistent electronic spectra and total energies obtained from the GW approximation with those from an extended GWGamma scheme that includes a nontrivial vertex function…
We provide an in-depth examination of the $GW$ approximation of Green's function many-body perturbation theory by detailing both its theoretical and practical aspects in the realm of quantum chemistry. First, the quasiparticle context is…
Atomic hydrogen provides a unique test case for computational electronic structure methods, since its electronic excitation energies are known analytically. With only one electron, hydrogen contains no electronic correlation and is…
The GW approximation is a cornerstone of many-body perturbation theory for computing single-particle excitations, yet it fundamentally breaks down in strongly correlated systems where the single-reference picture fails. To overcome this…
The vertex function ($\Gamma$) within the Green's function formalism encapsulates information about all higher-order electron-electron interaction beyond those mediated by density fluctuations. Herein, we present an efficient approach that…
Many-body perturbation theory (MBPT) based on Green's functions and Feynman diagrams provides a fundamental theoretical framework for various \emph{ab initio} computational approaches in molecular and materials science, including the random…
We propose an alternative formulation of Many-Body Perturbation Theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, that leads to excellent…
Hedin's scheme is solved with the inclusion of the vertex function ($GW\Gamma$) for a set of small molecules. The computational scheme allows for the consistent inclusion of the vertex both at the polarizability level and in the…
We introduce the $\Sigma^{\text{BSE}}@L^{\text{BSE}}$ self-energy in the quasi-particle self-consistent $GW$ (qs$GW$) framework (qs$\Sigma^{\text{BSE}}@L^{\text{BSE}}$). Here, $L$ is the two-particle response function which we calculate by…
Based on an exact functional form derived for the three-point vertex function $\Gamma$, we propose a self-consistent calculation scheme for the electron self-energy with $\Gamma$ always satisfying the Ward identity. This scheme is basically…
Ab initio many-body perturbation theory within the $GW$ approximation is a Green's function formalism widely used in the calculation of quasiparticle excitation energies of solids. In what has become an increasingly standard approach,…
The total energy and electron addition and removal spectra can in principle be obtained exactly from the one-body Green's function. In practice, the Green's function is obtained from an approximate self-energy. In the framework of many-body…
Starting with Hedins equations, simple expressions for the irreducible self-energy are derived. The derivation with vertex effects included in the self-energy results in a number of terms beyond GW such as second-order screened exchange…
Coupled-cluster (CC) theory and Green's function many-body perturbation theory (MBPT) have long evolved as distinct yet complementary frameworks for describing electronic correlation. While CC methods employ exponential wavefunction…
The automation of ab initio simulations is essential in view of performing high-throughput (HT) computational screenings oriented to the discovery of novel materials with desired physical properties. In this work, we propose algorithms and…
Several widely used methods for the calculation of band structures and photo emission spectra, such as the GW approximation, rely on Many-Body Perturbation Theory. They can be obtained by iterating a set of functional differential equations…
We present a diagrammatic approach to construct self-energy approximations within many-body perturbation theory with positive spectral properties. The method cures the problem of negative spectral functions which arises from a…
The $GW$ approximation has become a method of choice for predicting quasiparticle properties in solids and large molecular systems, owing to its favorable accuracy-cost balance. However, its accuracy is the result of a fortuitous…
This study examines how the GW approximation, one of the techniques covered by Green's functions and on many-body approximations (GFMBA), fares compared to the treatment of the Hubbard model solved using an exact diagonalization (ED)…