Convergence Properties of Fully Dressed Diagrammatic Series and Pathologies of the Luttinger-Ward Functional

We access the entire high-order diagrammatic series in terms of the fully dressed Green’s function G and the fully dressed screened interaction W by means of the Diagrammatic Monte Carlo method, and explore its convergence properties in connection with the recently discovered multivaluedness of the Luttinger-Ward functional for Hubbard-like models. In particular, we find that the G-W series diverges well below the branching point of the Luttinger-Ward functional, but admits analytic continuation beyond its convergence radius by standard techniques. We further explore the possibility of using fully dressed skeleton diagrammatic series in the strongly correlated regime to obtain precise results with controlled accuracy.