Dual boson approach to collective excitations in correlated fermionic systems

TL;DR

This paper introduces a dual boson approach that unifies the description of fermionic particles and collective excitations in correlated lattice systems, extending existing theories and enabling accurate calculations of magnetic and charge phenomena.

Contribution

It develops a comprehensive dual boson formalism that incorporates local and non-local interactions, extending EDMFT and providing a conserving approximation for collective excitations.

Findings

Derives a general expression for plasmonic dispersion in correlated media.

Shows that dual ladder summation improves beyond EDMFT.

Demonstrates effective superexchange interactions in the Hubbard model.

Abstract

We develop a general theory of a boson decomposition for both local and non-local interactions in lattice fermion models which allows us to describe fermionic degrees of freedom and collective charge and spin excitations on equal footing. An efficient perturbation theory in the interaction of the fermionic and the bosonic degrees of freedom is constructed in so-called dual variables in the path-integral formalism. This theory takes into account all local correlations of fermions and collective bosonic modes and interpolates between itinerant and localized regimes of electrons in solids. The zero-order approximation of this theory corresponds to extended dynamical mean-field theory (EDMFT), a regular way to calculate nonlocal corrections to EDMFT is provided. It is shown that dual ladder summation gives a conserving approximation beyond EDMFT. The method is especially suitable for consideration of collective magnetic and charge excitations and allows to calculate their renormalization with respect to "bare" RPA-like characteristics. General expression for the plasmonic dispersion in correlated media is obtained. As an illustration it is shown that effective superexchange interactions in the half-filled Hubbard model can be derived within the dual-ladder approximation.