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Recently, ab initio techniques have been successfully connected to thetraditional valence-space shell model. In doing so, they can either explicitlyprovide ab initio shell-model effective Hamiltonians or constrain theconstruction of empirical ones. In the present work, the possibility to followa similar path for the nuclear energy density functional (EDF) method isanalyzed. For this connection to be actualized, two theoretical techniques areinstrumental: the recently proposed ab initio PGCM-PT many-body formalism andthe MR-IMSRG pre-processing of the nuclear Hamiltonian. Based on both formalarguments and numerical results, possible new lines of research are brieflydiscussed, namely to compute ab initio EDF effective Hamiltonians at lowcomputational cost, to constrain empirical ones or to produce them directly viaan effective field theory that remains to be invented.

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