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 arises as an approximation to the Hedin equations. In Section 3.2, we briefly present some typical GW results for materials, including quasiparticle renormalizations, lifetimes, and band gap enhancements. In Section 4, the combination of GW and DMFT is summarized. Finally, as a prospective outlook, ab initio dynamical vertex approximation D $Γ$ A is introduced in Section 5 as a unifying scheme for all that: GW, DMFT and non-local vertex correlations beyond.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 arises as an approximation to the Hedin equations. In Section 3.2, we briefly present some typical GW results for materials, including quasiparticle renormalizations, lifetimes, and band gap enhancements. In Section 4, the combination of GW and DMFT is summarized. Finally, as a prospective outlook, ab initio dynamical vertex approximation D$Γ$A is introduced in Section 5 as a unifying scheme for all that: GW, DMFT and non-local vertex correlations beyond.

arXiv:1109.3972Sep 19, 20118 citations

The WKB Approximation

K. T. Hecht

Graduate texts in contemporary physicsJan 1, 20000 citations

Exact and many-body perturbation solutions of the Hubbard model applied to linear chains

Antoine Honet, Luc Henrard, Vincent Meunier

This study reports on the accuracy of the GW approximation for the treatment of the Hubbard model compared to exact diagonalization (ED) results. We consider not only global quantities, such as the total energy and the density of states, but also the spatial and spin symmetry of wavefunctions via the analysis of the local density of states. GW is part of the more general Green’s function approach used to develop many-body approximations. We show that, for small linear chains, the GW approximation corrects the mean-field (MF) approach by reducing the total energy and the magnetization obtained from the MF approximation. The GW energy gap is in better agreement with ED, especially in systems of an even number of atoms where, in contrast to the MF approximation, no plateau is observed below the artificial predicted phase transition. In terms of density of states, the GW approximation induces quasi-particles and side satellite peaks via a splitting process of MF peaks. At the same time, GW slightly modifies the localization (e.g., edges or center) of states. We also use the GW approximation results in the context of Löwdin’s symmetry dilemma and show that GW predicts an artificial paramagnetic–antiferromagnetic phase transition at a higher Hubbard parameter than MF does.This study reports on the accuracy of the GW approximation for the treatment of the Hubbard model compared to exact diagonalization (ED) results. We consider not only global quantities, such as the total energy and the density of states, but also the spatial and spin symmetry of wavefunctions via the analysis of the local density of states. GW is part of the more general Green’s function approach used to develop many-body approximations. We show that, for small linear chains, the GW approximation corrects the mean-field (MF) approach by reducing the total energy and the magnetization obtained from the MF approximation. The GW energy gap is in better agreement with ED, especially in systems of an even number of atoms where, in contrast to the MF approximation, no plateau is observed below the artificial predicted phase transition. In terms of density of states, the GW approximation induces quasi-particles and side satellite peaks via a splitting process of MF peaks. At the same time, GW slightly modifies the localization (e.g., edges or center) of states. We also use the GW approximation results in the context of Löwdin’s symmetry dilemma and show that GW predicts an artificial paramagnetic–antiferromagnetic phase transition at a higher Hubbard parameter than MF does.

arXiv:2111.13536AIP AdvancesMar 1, 202211 citations

Γ

A is introduced in Section 5 as a unifying scheme for all that: GW, DMFT and non-local vertex correlations beyond.