Dynamical mean-field theory describes the impact of strong local correlation
effects in many-electron systems. While the single-particle spectral function
is directly obtained within the formalism, two-particle susceptibilities can
also be obtained by solving the Bethe-Salpeter equation. The solution requires
handling infinite matrices in Matsubara frequency space. This is commonly
treated using a finite frequency cut-off, resulting in slow linear convergence.
We show that decomposing the two-particle response in local and non-local
contributions enables a reformulation of the Bethe-Salpeter equation inspired
by the dual boson formalism. The re-formulation has a drastically improved
cubic convergence with respect to the frequency cut-off, facilitating the
calculation of susceptibilities in multi-orbital systems considerably. The dual
Bethe-Salpeter equation uses the fully reducible vertex which is free from
vertex divergences. We benchmark the approach on several systems including the
spin susceptibility of strontium ruthenate Sr2βRuO4β, a strongly correlated
Hund's metal with three active orbitals. We propose the dual Bethe-Salpeter
equation as a new standard for calculating two-particle response within
dynamical mean-field theory