Scrutinizing $GW$-based methods using the Hubbard dimer

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 i) 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; ii) the BSE formalism yields accurate correlation energies over a wide range of $U$ when the trace (or plasmon) formula is employed; iii) 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); iv) the trace formula has the correct behavior for weak (\ie, small $U$) interaction, unlike the ACFDT expression.

arXiv comment12 pages, 4 figures

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• A regularized second-order correlation method from Green's function theory
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• Combining Localized Orbital Scaling Correction and Bethe-Salpeter Equation for Accurate Excitation Energies
• Renormalized Singles with Correlation in $GW$ Green's Function Theory for Accurate Quasiparticle Energies
• GW with hybrid functionals for large molecular systems
• On Green's function embedding using sum-over-pole representations
• Uncovering relationships between the electronic self-energy and coupled-cluster doubles theory
• Orbital-Free Quasi-Density Functional Theory
• Broken symmetry solutions in one-dimensional lattice models via many-body perturbation theory