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

TL;DR

The paper introduces a dual Bethe-Salpeter equation reformulation within dynamical mean-field theory that significantly improves the convergence rate for calculating two-particle susceptibilities in multi-orbital systems.

Contribution

It presents a novel reformulation inspired by the dual boson formalism that enhances convergence and simplifies susceptibility calculations in complex multi-orbital models.

Findings

Achieves cubic convergence with respect to frequency cut-off.

Successfully benchmarks on Sr2RuO4, a strongly correlated Hund's metal.

Uses fully reducible vertex free from divergences.

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.