Dresden 2014 – wissenschaftliches Programm

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HL: Fachverband Halbleiterphysik

HL 84: Poster: Electronic structure theory / Carbon (other than graphene) / Si, Ge, and SiC / III-V semiconductors (other than nitrides)

HL 84.1: Poster

Mittwoch, 2. April 2014, 17:00–20:00, P1

Analytic evaluation of the electronic self-energy in the GW approximation for two electrons on a sphere — •Arno Schindlmayr — Department Physik, Universität Paderborn, 33095 Paderborn, Germany

The GW approximation for the electronic self-energy is a very important tool for the quantitative prediction of excited states in solids. However, its mathematical exploration has been hampered by the fact that it must, in general, be evaluated numerically even for very simple systems. Here I describe a nontrivial continuum model, consisting of two interacting electrons on the surface of a sphere, and show that a completely analytic derivation of the GW self-energy, in the absence of self-consistency, is possible in this case. In contrast to lattice Hubbard models with the same property, the electron dynamics are governed by the normal long-range Coulomb potential instead of a short-range onsite interaction, the strength of the correlation can be controlled by a natural physical parameter, the sphere radius, and the infinite Hilbert space of one-particle states is not truncated. Therefore, the analytic expression for the self-energy can be used to study 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 obtained asymptotic formula shows that the truncation error is dominated by a term proportional to the cutoff energy to the power −3/2, which is compatible with earlier numerical results for band gaps in real materials.