Rooting the EDF method into the ab initio framework. PGCM-PT formalism based on MR-IMSRG pre-processed Hamiltonians

Recently, ab initio techniques have been successfully connected to the traditional valence-space shell model. In doing so, they can either explicitly provide ab initio shell-model effective Hamiltonians or constrain the construction of empirical ones. In the present work, the possibility to follow a similar path for the nuclear energy density functional (EDF) method is analyzed. For this connection to be actualized, two theoretical techniques are instrumental: the recently proposed ab initio PGCM-PT many-body formalism and the MR-IMSRG pre-processing of the nuclear Hamiltonian. Based on both formal arguments and numerical results, possible new lines of research are briefly discussed, namely to compute ab initio EDF effective Hamiltonians at low computational cost, to constrain empirical ones or to produce them directly via an effective field theory that remains to be invented.