  We construct valence-space Hamiltonians for use in shell-model calculations,
where the residual two-body interaction is based on symmetry principles and the
low-momentum expansion from chiral effective field theory. In addition to the
usual free-space contact interactions, we also include novel
center-of-mass--dependent operators that arise due to the Galilean invariance
breaking by in-medium effects. We fitted the low-energy constants to 441
ground- and excited-state energies in the sd shell and obtained a
root-mean-square derivation of 1.8 MeV at leading order and of 0.5 MeV at
next-to-leading order, with natural low-energy constants in all cases. The
developed chiral shell-model interactions enable order-by-order uncertainty
estimates and show promising predictions for neutron-rich isotopes beyond the
fitted data set.
