Efficient Bethe-Salpeter equations' treatment in dynamical mean-field theory

TL;DR

This paper introduces two new schemes to correct high-frequency truncation errors in Bethe-Salpeter equations, enhancing the accuracy of dynamical mean-field theory calculations, especially for complex multi-orbital systems.

Contribution

The authors develop and demonstrate two alternative schemes that improve the treatment of Bethe-Salpeter equations within DMFT, applicable across all bosonic frequencies and channels.

Findings

Schemes effectively reduce high-frequency truncation errors.

Application to Anderson impurity models shows improved accuracy.

Potential to enhance multi-orbital DMFT calculations.

Abstract

We present here two alternative schemes designed to correct the high-frequency truncation errors in the numerical treatment of the Bethe-Salpeter equations. The schemes are applicable to all Bethe-Salpeter calculations with a local two-particle irreducible local, which is relevant, e.g., for the dynamical mean-field theory (DMFT) and its diagrammatic extensions. In particular, within a purely diagrammatic framework, we could extend existing algorithms for treating the static case in the particle-hole sector to more general procedures applicable to all bosonic frequencies and all channels. After illustrating the derivation and the theoretical interrelation of the two proposed schemes, these have been applied to the Bethe-Salpeter equations for the auxiliary Anderson impurity models of selected DMFT calculations, where results can be compared against a numerically "exact" solution. The successful performance of the proposed schemes suggests that their implementation can significantly improve the accuracy of dynamical mean-field theory (DMFT) calculations at the two-particle level, in particular for more realistic multi-orbital calculations where the large number of degrees of freedom substantially restricts the actual frequency range for numerical calculations, as well as -on a broader perspective- of the diagrammatic extensions of DMFT.