Equivalence of model space techniques and the renormalization group for a separable model problem

Lee–Suzuki similarity transformations and Krenciglowa–Kuo folded diagrams are two common methods used to derive energy independent model space effective interactions for nuclear many-body systems. We demonstrate that these two methods are equivalent to a Renormalization Group (RG) analysis of a well-studied problem in quantum mechanics. The effective low-momentum potentials Veff obtained from model space methods are shown to obey the same scaling equation for Veff that RG arguments predict. This indicates that model space methods might be of interest to those studying low-energy nuclear physics using Effective Field Theories (EFT). We find the new result that all of the different energy independent model space techniques yield a unique low-momentum Veff when applied to the toy model under consideration.