This paper introduces a new computational method to calculate tiny nuclear quantities that break parity symmetry. Those quantities include the nuclear anapole moment and the Schiff moment. Both are important because they connect atomic and nuclear measurements to fundamental symmetries of nature and to possible physics beyond the Standard Model. Until now, accurate ‘‘first‑principles’’ (ab initio) calculations for the medium‑mass and heavy nuclei most relevant to experiments were not available.

The authors generalize a many‑body tool called the in‑medium similarity renormalization group (IMSRG). IMSRG works by continuously transforming the nuclear Hamiltonian so that the low‑energy part becomes easier to solve. The new version, which they call the parity‑violating IMSRG (PV‑IMSRG), evolves the tiny parity‑violating interaction and the relevant parity‑violating operators together with the usual strong nuclear Hamiltonian. Doing so avoids the need to explicitly sum over a large number of opposite‑parity excited states, a step that is hard or impossible for heavy nuclei.

Technically, the method treats the parity‑violating interaction as a small perturbation and keeps only the leading terms that matter. The authors write coupled flow equations that move both the strong and weak parts through the same unitary transformation and then drop terms that are second order in the tiny interaction. They implement the approach in a valence‑space IMSRG framework using the imsrg++ code and diagonalize the resulting effective Hamiltonian with the Kshell shell‑model code. They benchmark the method against the no‑core shell model in light nuclei and report the first ab initio predictions for the anapole moment in 29Si and for Schiff moments in 129Xe. For the parity‑violating nucleon–nucleon interaction they use the phenomenological Desplanques–Donoghue–Holstein (DDH) potential with updated parameters, and they note that chiral effective field theory potentials will be implemented in future work.