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arXiv · 2306.05157

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

Erik G. C. P. van Loon·Hugo U. R. Strand
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Abstract

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. A decomposition of 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. 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 Sr$_2$RuO$_4$, a strongly correlated Hund's metal with three active orbitals.

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Erik G. C. P. van Loon, Hugo U. R. Strand. 2023-06-08. Dual Bethe-Salpeter equation for the multi-orbital lattice susceptibility within dynamical mean-field theory. https://doi.org/10.1103/physrevb.109.155157

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