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We propose an efficient dual boson scheme, which extends the DMFT paradigm tocollective excitations in correlated systems. The theory is fullyself-consistent both on the one- and on the two-particle level, thus describingthe formation of collective modes as well as the renormalization of electronicand bosonic spectra on equal footing. The method employs an effective impuritymodel comprising both fermionic and bosonic hybridization functions. Onlysingle- and two-electron Green's functions of the reference problem enter thetheory, due to the optimal choice of the self-consistency condition for theeffective bosonic bath. We show that the theory is naturally described by adual Luttinger-Ward functional and obeys the relevant conservation laws.

Self-consistent Dual Boson approach to single-particle and collective excitations in correlated systems