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

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 cutoff, resulting in slow linear convergence. A decomposition of the two-particle response in local and nonlocal contributions enables a reformulation of the Bethe-Salpeter equation inspired by the dual boson formalism. The reformulation has a drastically improved cubic convergence with respect to the frequency cutoff, considerably facilitating the calculation of susceptibilities in multi-orbital systems. This improved convergence arises from the fact that local contributions can be measured in the impurity solver. 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>Sr</a:mi><a:mn>2</a:mn></a:msub><a:msub><a:mi>RuO</a:mi><a:mn>4</a:mn></a:msub></a:mrow></a:math>, a strongly correlated Hund's metal with three active orbitals.