Exploring Singular Value Decompositions within the In-Medium Similarity Renormalization Group Framework

One of the main challenges for ab initio nuclear many-body theory in the coming decade is the growth of computational and storage costs as calculations are extended to increasingly heavy, exotic and structurally complex nuclei. Here we investigate the factorization of nuclear interactions in m-scheme as a mean to address this issue. We perform Singular Value Decompositions of nuclear Hamiltonians in normal-ordered form and develop and implement their In-Medium Similarity Renormalization Group (IMSRG) evolution in term of the relevant singular values

We discuss structural features of the Hamiltonians that emerge upon their projection into suitably chosen low-rank space, and show that a small number of relevant components from the first space can be sufficient to capture important characteristics of the evolution. We also explore implications for the storage and computational complexity of the IMSRG framework.