Description of quasiparticle and satellite properties via cumulant expansions of the retarded one-particle Green's function

Abstract

A new cumulant-based $GW$ approximation for the retarded one-particle Green's function is proposed, motivated by an exact relation between the improper Dyson self-energy and the cumulant generating function. Qualitative aspects of this method are explored within a simple one-electron independent phonon model, where it is seen that the method preserves the energy moment of the spectral weight while also reproducing the exact Green's function in the weak coupling limit. For the three-dimensional electron gas, this method predicts multiple satellites at the bottom of the band, albeit with inaccurate peak spacing. However, its quasiparticle properties and correlation energies are more accurate than both previous cumulant methods and standard $G_0{W}_0$. Our results point to new features that may be exploited within the framework of cumulant-based methods and suggest promising directions for future exploration and improvement of cumulant-based $GW$ approaches.

arXiv comment7 pages

References in corpus (14)

• The GW method
• Quasiparticle Self-Consistent GW Theory
• The valence electron photoemission spectrum of semiconductors: ab initio description of multiple satellites
• Many-body perturbation theory using the density-functional concept: beyond the GW approximation
• Physical origin of satellite in photoemission of doped graphene: An ab-initio GW plus cumulant study
• Many-body quantum chemistry for the electron gas: convergent perturbative theories
• Spectral Functions of the Uniform Electron Gas via Coupled-Cluster Theory and Comparison to the $GW$ and Related Approximations
• Band structures of plasmonic polarons
• The momentum distribution of the homogeneous electron gas
• On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands
• Spectral Fingerprints of Electron-Plasmon Coupling
• Satellite structures in the spectral functions of semiconductor quantum well two-dimensional electron gases: a GW plus cumulant study
• Momentum distribution and Compton profile by the ab initio GW approximation
• Dispersion and lineshape of plasmon satellites in one, two and three dimensions

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• Dynamically screened vertex correction to $GW$
• Vertex corrections for positive-definite spectral functions of simple metals
• One-electron spectra and susceptibilities of 3D electron gas from self-consistent solutions of Hedin's equations
• Quasiparticle spectra from molecules to bulk
• A unified Green's function approach for spectral and thermodynamic properties from algorithmic inversion of dynamical potentials
• Low-energy peak in the one-particle spectral function of the electron gas at metallic densities