Related papers: Hedin's equations and enumeration of Feynman's dia…
The many-body dynamics of interacting electrons in condensed matter and quantum chemistry is often studied at the quasiparticle level, where the perturbative diagrammatic series is partially resummed. Based on Hedin's equations for…
In many ways the solution to the Hedin equations represents an exact solution to the many body problem. However, for most systems of practical interest, the solution to the Hedin equations is rendered nearly numerically intractable because…
We present an iterative algorithm to count Feynman diagrams via many-body relations. The algorithm allows us to count the number of diagrams of the exact solution for the general fermionic many-body problem at each order in the interaction.…
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…
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…
A derivation is given of the Feynman rules to be used in the perturbative computation of the Green's functions of a generic quantum many-body theory when the action which is being perturbed is not necessarily quadratic. Some applications…
The gap equation for fermions in a version of thermal QED in three dimensions is studied numerically in the Schwinger-Dyson formalism. The interest in this theory has been recently revived since it has been proposed as a model of…
We present a new method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important…
The solution of some equations involving functional derivatives is given as a series indexed by planar binary trees. The terms of the series are given by an explicit recursive formula. Some algebraic properties of these series are…
We present a general procedure for obtaining progressively more accurate functional expressions for the electron self-energy by iterative solution of Hedin's coupled equations. The iterative process starting from Hartree theory, which gives…
Information about the number of Feynman graphs for a given physical process in a given field theory is especially useful for confirming the result of a Feynman graph generator used in an automatic system of perturbative calculations. A…
We completely generalize previous results related to the counting of connected Feynman diagrams. We use a generating function approach, which encodes the Wick contraction combinatorics of the respective connected diagrams. Exact solutions…
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…
Functional Schr\"{o}dinger equations for interacting fields are solved via rigorous non-perturbative Feynman type integrals.
We extend the self-consistent Green's functions formalism to take into account three-body interactions. We analyze the perturbative expansion in terms of Feynman diagrams and define effective one- and two-body interactions, which allows for…
Historically, the GW approach was put forward by Hedin as the simplest approximation to the so-called Hedin equations. In Section 2, we will derive these Hedin equations from a Feynman-diagrammatical point of view. Section 3.1 shows how GW…
Within many-body perturbation theory, Hedin's formalism offers a systematic way to iteratively compute the self-energy $\Sigma$ of any interacting system, provided one can evaluate the interaction vertex $\Gamma$ exactly. This is however…
Hedin's $GW$ approximation to the electronic self-energy has been impressively successful to calculate quasiparticle energies, such as ionization potentials, electron affinities, or electronic band structures. The success of this fairly…
We argue that the Mellin-Barnes representations of Feynman diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman diagrams with arbitrary powers of propagators without recourse to…
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…