In-medium similarity renormalization group for closed and open-shell nuclei

We present a pedagogical introduction to the in-medium similarity renormalization group (IMSRG) framework for ab initio calculations of nuclei. The IMSRG performs continuous unitary transformations of the nuclear many-body Hamiltonian in second-quantized form, which can be implemented with polynomial computational effort. Through suitably chosen generators, it is possible to extract eigenvalues of the Hamiltonian in a given nucleus, or drive the Hamiltonian matrix in configuration space to specific structures, e.g., band-or block-diagonal form. Exploiting this flexibility, we describe two complementary approaches for the description of closed-and open-shell nuclei: the first is the multireference IMSRG (MR-IMSRG), which is designed for the efficient calculation of nuclear ground-state properties. The second is the derivation of non-empirical valence-space interactions that can be used as input for nuclear shell model (i.e., configuration interaction (CI)) calculations. This IMSRG+shell model approach provides immediate access to excitation spectra, transitions, etc, but is limited in applicability by the factorial cost of the CI calculations. We review applications of the MR-IMSRG and IMSRG+shell model approaches to the calculation of ground-state properties for the oxygen, calcium, and nickel isotopic chains or the spectroscopy of nuclei in the lower sd shell, respectively, and present selected new results, e.g., for the ground-and excited state properties of neon isotopes.