Interplay between local response and vertex divergences in many-fermion systems with on-site attraction
Daniel Springer, Patrick Chalupa-Gantner, S. Ciuchi, Giorgio Sangiovanni, A. Toschi
Abstract
Surprising singularities occur, almost ubiquitously, when inverting the Bethe-Salpeter equations of fundamental many-fermion models. For systems with repulsive interactions, they were interpreted as nonperturbative manifestations of a progressive suppression of fluctuations. By studying here the case of attractive interactions, the authors provide a counterexample to this interpretation: they find that singularities also affect a dominant sector of the attractive model, the charge channel. The fact that singularities are not confined to suppressed sectors poses additional challenges to the many-fermion theory, whose clarification calls for dedicated studies in the near future.