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.

12 pages, 4 figures

References in corpus (15)

• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation
• The Bethe-Salpeter Equation Formalism: From Physics to Chemistry
• Towards GW Calculations on Thousands of Atoms
• Correlation energy expressions from the adiabatic-connection fluctuation-dissipation theorem approach
• Range-separated density-functional theory with random phase approximation: detailed formalism and illustrative applications
• Fully self-consistent $GW$ and quasi-particle self-consistent $GW$ for molecules
• Bond Breaking and Bond Formation: How Electron Correlation is Captured in Many-Body Perturbation Theory and Density-Functional Theory
• Beyond the GW approximation: combining correlation channels
• Static correlation and electron localization in molecular dimers from the self-consistent RPA and GW approximation
• Separable Resolution-of-the-Identity with All-Electron Gaussian Bases: Application to Cubic-scaling RPA
• Correlation energy within exact-exchange ACFD theory: systematic development and simple approximations
• Renormalized Singles Green's Function in the T-Matrix Approximation for Accurate Quasiparticle Energy Calculation
• Dynamical Correction to the Bethe-Salpeter Equation Beyond the Plasmon-Pole Approximation
• Photoemission Spectra from Reduced Density Matrices: the Band Gap in Strongly Correlated Systems