  Halide double perovskites with alternating silver and pnictogen cations are
an emerging family of photoabsorber materials with robust stability and band
gaps in the visible range. However, the nature of optical excitations in these
systems is not yet well understood, limiting their utility. Here, we use ab
initio many-body perturbation theory within the $GW$ approximation and the
Bethe-Salpeter equation approach to calculate the electronic structure and
optical excitations of the double perovskite series Cs$_2$AgBX$_6$, with
B=Bi$^{3+}$, Sb$^{3+}$, X = Br$^-$, Cl$^-$. We find that these materials
exhibit strongly localized resonant excitons with energies from 170 to 434 meV
below the direct band gap. In contrast to lead-based perovskites, the
Cs$_2$AgBX$_6$ excitons are computed to be non-hydrogenic, with anisotropic
effective masses and sensitive to local field effects, a consequence of their
chemical heterogeneity. Our calculations demonstrate the limitations of the
Wannier-Mott and Elliott models for this class of double perovskites and
contribute to a detailed atomistic understanding of their light-matter
interactions.
