Analytic evaluation of the electronic self-energy in the GW approximation for two electrons on a sphere

Abstract

The GW approximation for the electronic self-energy is an important tool for the quantitative prediction of excited states in solids, but its mathematical exploration is hampered by the fact that it must, in general, be evaluated numerically even for very simple systems. In this paper I describe a nontrivial model consisting of two electrons on the surface of a sphere, interacting with the normal long-range Coulomb potential, and show that the GW self-energy, in the absence of self-consistency, can in fact be derived completely analytically in this case. The resulting expression is subsequently used to analyze the convergence of the energy gap between the highest occupied and the lowest unoccupied quasiparticle orbital with respect to the total number of states included in the spectral summations. The asymptotic formula for the truncation error obtained in this way, whose dominant contribution is proportional to the cutoff energy to the power -3/2, may be adapted to extrapolate energy gaps in other systems.

8 pages including 3 figures

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Cited by in corpus (8)

• Predictive GW calculations using plane waves and pseudopotentials
• Accurate all-electron $G_0{W}_0$ quasiparticle energies employing the full-potential augmented planewave method
• Converged GW quasiparticle energies for transition metal oxide perovskites
• Green functions and self-consistency: insights from the spherium model
• Towards high-throughput many-body perturbation theory: efficient algorithms and automated workflows
• Gap control in phosphorene/BN structures from first principles calculations
• Exact wave functions for concentric two-electron systems
• Transient Uniform Electron Gases