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The STLS Theory for the Five-dimensional Homogeneous Electron Gas

Authors: Le Viet Duc Pham

Ref.: Bachelor thesis, Martin-Luther University of Halle-Wittenberg (2021)

Abstract: The sufficiency of the STLS theory, especially at metallic densities, was proven in a wide variety of research. The inclusion of the pair correlation function in the ansatz for the two-particle density in the phase space leads to the local field correction G(q) which takes the short-range interaction beyond the RPA into consideration. This provides a new dielectric function for the study of the HEG through the dielectric formulation. The computational cost of the algorithm is also low as all integrals needed for the calculation are one-dimensional integrals. In this thesis, we successfully established a set of equations for the calculation in the five- dimensional case. In order to fully expand the theory to arbitrary dimension we need to evaluate the integrals in the general D-dimensional case for the real part of the Lindhard Polarizability and the local field correction in the Hartree-Fock approximation. These questions will be furthermore studied in detail.

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