  The quasi-particle band structure and dielectric function for the so-called
magic sequence SiGe$_2$Si$_2$Ge$_2$SiGe$_{12}$ (or $\alpha_{12}$) structure
[PRL 108, 027401 (2012)] are calculated by many-body perturbation theory (MBPT)
within an ab-initio framework. On top of density functional calculations within
the local density approximation (LDA) leading to a fundamental band gap of 0.23
eV, we have computed the quasi-particle band structure within the G$_0$W$_0$
approach opening the gap to 0.61 eV. Moreover, we have calculated the optical
properties by solving the Bethe-Salpeter equation (BSE) for the electron-hole
two-particle correlation function. When comparing the imaginary part of the
dielectric function obtained at various levels of approximation, \emph{i.e.}
the independent particle approximation (or random phase approximation) based on
(i) the LDA or (ii) GW band structures, and (iii) the BSE including local field
effects and electron-hole correlations, we observe that the important first
transition is better explained with taking into account excitonic effects.
Moreover, the onset transition originating from the direct transition of the
magic sequence structure is also investigated.
