  We extend the weak-coupling diagrammatic determinantal algorithm to
projective schemes as well as to the inclusion of phonon degrees of freedom.
The projective approach provides a very efficient algorithm to access zero
temperature properties. To implement phonons, we integrate them out in favor of
a retarded density-density interaction and simulate the resulting purely
electronic action with the weak-coupling diagrammatic determinantal algorithm.
Both extensions are tested within the dynamical mean field approximation for
the Hubbard and Hubbard-Holstein models.
