Topological Index and Homotopy in Coupled-Cluster theory

We propose a comprehensive mathematical framework for Coupled-Cluster-type methods based on topological degree theory. This allows us to establish more general existence results than Schneider's and deduce local information about the solutions of the CC equations. The idea of constructing a homotopy for CC theory is not new, and has been extensively studied in the past. We consider the more recent Kowalski--Piecuch (KP) homotopy from a mathematical point of view and use it as a theoretical tool to prove the existence of a truncated CC solution. This follows from a more general result guaranteeing the existence of a whole solution curve of the KP homotopy.