  Recent studies of dynamical screening of the electronic Coulomb interactions
in solids have revived interest in lattice models of correlated fermions
coupled to bosonic degrees of freedom (Hubbard-Holstein-type models). We
propose a dynamical mean-field-based approach to dynamically screened Coulomb
interactions. In the effective Anderson-Holstein model, a transformation to
slave rotors [S. Florens and A. Georges, Phys. Rev. B 66, 165111 (2002)] is
performed to decouple the dynamical part of the interaction. This
transformation allows for a systematic derivation and analysis of recently
introduced approximate schemes for the solution of dynamical impurity problems,
in particular, the Bose factor ansatz within the dynamic atomic limit
approximation (DALA) with and without Lang-Firsov correction. More importantly
still, it suggests an optimized choice for a Bose factor in the sense of the
variational principle of Feynman and Peierls. We demonstrate the accuracy of
our scheme and present a comparison to calculations within the DALA.
