No abstract

We design an efficient and balanced approach that captures major effects of collective electronic fluctuations in strongly correlated fermionic systems using a simple diagrammatic expansion on a basis of dynamical meanfield theory. For this aim we perform a partial bosonization of collective fermionic fluctuations in leading channels of instability. We show that a simultaneous account for different bosonic channels can be done in a consistent way that allows to avoid the famous Fierz ambiguity problem. The present method significantly improves a description of an effective screened interaction W in both, charge and spin channels, and has a great potential for application to realistic GW-like calculations for magnetic materials.

In this work we present a comprehensive analysis of collective electronic fluctuations and their effect on single-particle properties of the Hubbard model. Our approach is based on a standard dual fermion/boson scheme with the interaction truncated at the two-particle level. Within this framework we compare various approximations that differ in the set of diagrams (ladder vs exact diagrammatic Monte Carlo), and/or in the form of the four-point interaction vertex (exact vs partially bosonized). This allows to evaluate the effect of all components of the four-point vertex function on the electronic self-energy. In particular, we observe that contributions that are not accounted for by the partially bosonized approximation for the vertex have only a minor effect on electronic degrees of freedom in a broad range of model parameters. In addition, we find that in the regime, where the ladder dual fermion approximation provides an accurate solution of the problem, the leading contribution to the self-energy is given by the longitudional bosonic modes. This can be explained by the fact that contributions of transverse particle-hole and particle-particle modes partially cancel each other. Our findings justify applicability of the recently introduced dual triply irreducible local expansion (D-TRILEX) method that provides one of the simplest consistent diagrammatic extensions of the dynamical mean-field theory.