Coupled-Cluster Theory Revisited

We propose a comprehensive mathematical framework for Coupled-Cluster-type methods. These aim at accurately solving the many-body Schr\"odinger equation. The present work has two main aspects. First, we rigorously describe the discretization scheme involved in Coupled-Cluster methods using graph-based concepts. This allows us to discuss different methods in a unified and more transparent manner, including multireference methods. Second, we analyze the nonlinear equations of the single-reference Coupled-Cluster method using topological degree theory. We establish existence results and qualitative information about the solutions of these equations that also sheds light on some of the numerically observed behavior. For the truncated Coupled-Cluster method, we derive an energy error bound for approximate eigenstates of the Schr\"odinger equation.