Description
We discuss the algebra and combinatorics underpinning coupled cluster (CC) theory for quantum many-body systems. The high-dimensional eigenvalue problems that encode the electronic Schrödinger equation are approximated by polynomial systems at various levels of truncation. The exponential parametrization of the eigenstates gives rise to truncation varieties. These generalize Grassmannians in their Plücker embedding. We offer a detailed study of truncation varieties and their CC degrees, a complexity measure for solving the CC equations. We also discuss the solutions of the CC equations.
