Scrutinizing GW-Based Methods Using the Hubbard Dimer.

S Di Sabatino,P-F Loos,P Romaniello

doi:10.3389/fchem.2021.751054

Abstract

Using the simple (symmetric) Hubbard dimer, we analyze some important features of the GW approximation. We show that the problem of the existence of multiple quasiparticle solutions in the (perturbative) one-shot GW method and its partially self-consistent version is solved by full self-consistency. We also analyze the neutral excitation spectrum using the Bethe-Salpeter equation (BSE) formalism within the standard GW approximation and find, in particular, that 1) some neutral excitation energies become complex when the electron-electron interaction U increases, which can be traced back to the approximate nature of the GW quasiparticle energies; 2) the BSE formalism yields accurate correlation energies over a wide range of U when the trace (or plasmon) formula is employed; 3) the trace formula is sensitive to the occurrence of complex excitation energies (especially singlet), while the expression obtained from the adiabatic-connection fluctuation-dissipation theorem (ACFDT) is more stable (yet less accurate); 4) the trace formula has the correct behavior for weak (i.e., small U) interaction, unlike the ACFDT expression.

Highlights

Many-body perturbation theory (MBPT) based on Green’s functions is among the standard tools in condensed matter physics for the study of ground- and excited-state properties. (Aryasetiawan and Gunnarsson, 1998; Onida et al, 2002; Martin et al, 2016; Golze et al, 2019)
In the following we provide the key equations of MBPT (Martin et al, 2016) and, in particular, we discuss how one can calculate ground- and excited-state properties, namely removal and addition energies, spectral function, total energies, and neutral excitation energies
The two approaches have been recently compared at the randomphase approximation (RPA) level for the case of Be2, (Li et al, 2020), showing similar improved performances at the RPA@GW@PBE level with respect to the RPA@PBE level and an impressive accuracy by introducing BSE (BSE@GW@HF) correction in the trace formula

Summary

Introduction

Many-body perturbation theory (MBPT) based on Green’s functions is among the standard tools in condensed matter physics for the study of ground- and excited-state properties. (Aryasetiawan and Gunnarsson, 1998; Onida et al, 2002; Martin et al, 2016; Golze et al, 2019). The GW approximation (Hedin, 1965; Golze et al, 2019) has become the method of choice for bandstructure and photoemission calculations and, combined with the Bethe-Salpeter equation (BSE@ GW) formalism, (Salpeter and Bethe, 1951; Strinati, 1988; Albrecht et al, 1998; Rohlfing and Louie, 1998; Benedict et al, 1998; van der Horst et al, 1999a; Blase et al, 2018, 2020), for optical spectra calculations. Several studies of the performance of various flavors of GW in atomic and molecular systems are present in the literature,

Methods

Results

Conclusion