  Contractor Renormalization (CORE) is a numerical renormalization method for
Hamiltonian systems that has found applications in particle and condensed
matter physics. There have been few studies, however, on further understanding
of what exactly it does and its convergence properties. The current work has
two main objectives. First, we wish to investigate the convergence of the
cluster expansion for a two-dimensional Heisenberg Antiferromagnet(HAF). This
is important because the linked cluster expansion used to evaluate this formula
non-perturbatively is not controlled by a small parameter. Here we present a
study of three different blocking schemes which reveals some surprises and in
particular, leads us to suggest a scheme for defining successive terms in the
cluster expansion. Our second goal is to present some new perspectives on CORE
in light of recent developments to make it accessible to more researchers,
including those in Quantum Information Science. We make some comparison to
entanglement-based approaches and discuss how it may be possible to improve or
generalize the method.
