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Dynamical mean-field theory describes the impact of strong local correlationeffects in many-electron systems. While the single-particle spectral functionis directly obtained within the formalism, two-particle susceptibilities canalso be obtained by solving the Bethe-Salpeter equation. The solution requireshandling infinite matrices in Matsubara frequency space. This is commonlytreated using a finite frequency cut-off, resulting in slow linear convergence.We show that decomposing the two-particle response in local and non-localcontributions enables a reformulation of the Bethe-Salpeter equation inspiredby the dual boson formalism. The re-formulation has a drastically improvedcubic convergence with respect to the frequency cut-off, facilitating thecalculation of susceptibilities in multi-orbital systems considerably. The dualBethe-Salpeter equation uses the fully reducible vertex which is free fromvertex divergences. We benchmark the approach on several systems including thespin susceptibility of strontium ruthenate Sr$_2$RuO$_4$, a strongly correlatedHund's metal with three active orbitals. We propose the dual Bethe-Salpeterequation as a new standard for calculating two-particle response withindynamical mean-field theory.

Dual Bethe-Salpeter equation for the multi-orbital lattice susceptibility within dynamical mean-field theory