Revisting the Density Matrix Expansion with Regulated Chiral Interactions

The density matrix expansion provides a general way to map microscopic interactions to a local functional. Previous density matrix expansion formulations added unregulated chiral long-range potentials to a Skyrme-type functional, which accounted for the short-range contributions. We implement the expansion with new coordinate space regulators using the regulator cutoff as a tool to adiabatically turn on finite-range pion interactions. We discuss 'smoking guns' for correct inclusion of 3-body forces, which are implemented in a normal-ordering prescription, and compare to ab initio calculations.