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

References in corpus (8)

• Efficient implementation of the GW approximation within the all-electron FLAPW method
• Band convergence and linearization error correction of all-electron GW calculations: The extreme case of zinc oxide
• Beyond the GW approximation: combining correlation channels
• Two electrons on a hypersphere: a quasi-exactly solvable model
• Elimination of the linearization error in GW calculations based on the linearized augmented-plane-wave method
• Screening in 2D: GW calculations for surfaces and thin films using the repeated-slab approach
• Ground state of two electrons on a sphere
• Dielectric anisotropy in the GW space-time method