Factorization Methods and the Similarity Renormalization Group*

We perform Singular Value Decompositions of modern nucleon-nucleon inter- actions and implement their Similarity Renormalization Group (SRG) evolution directly in terms of the relevant singular vectors. We study the behavior of the singular value spectrum as a function of the resolution scales, and demon- strate that low-resolution interactions allow accurate low-rank approximations, using two-nucleon scattering phase shifts and the deuteron binding energies as benchmark observables.

A small number of singular components per partial wave are sufficient to capture the strong interaction and perform an accurate SRG evolution, while the Coulomb interaction requires special consideration. The rank is uniform across all partial waves, and depends only weakly on the basis choice in the tested cases.

We test the low-rank approximation to the SRG-evolved interactions in many- body calculations based on the In-Medium SRG. By including nuclear radii in our analysis, we verify that the implementation of the SRG using the singular vectors of the interaction does not spoil the consistent evolution of other observables.