Abstract
Based on the Hedin fundamental equations Bethe-Salpeter equations are derived for generalized four-point functions, the polarization function \(P\) and the density correlation function \(L\). Their integral kernels are characterized by the effective interaction between two particles or even modified by the Hartree response. Their inhomogeneities are given in random phase and independent-quasiparticle approximation, respectively. The kernels are further approximated within the GW approximation by the screened Coulomb potential \(W\). It leads to a summation over all ladder diagrams. The application of \(P\) to frequency-dependent optical properties is described. Only the spin-averaged function is needed. The inclusion of optical local-field effects yields a Bethe-Salpeter equation for the macroscopic polarization function \(P^M\) with an integral kernel that contains a short-range Coulomb interaction. The corresponding two-point quantity of \(P^M\) determines the macroscopic dielectric function.
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Bechstedt, F. (2015). Bethe-Salpeter Equations for Response Functions. In: Many-Body Approach to Electronic Excitations. Springer Series in Solid-State Sciences, vol 181. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44593-8_18
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DOI: https://doi.org/10.1007/978-3-662-44593-8_18
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