Beyond mean-field methods are very successful tools for the description of large-amplitude collective motion for even-even atomic nuclei. The state-of-the-art framework of these methods consists in a generator coordinate method based on angular-momentum and particle-number projected triaxially deformed Hartree-Fock-Bogoliubov (HFB) states. The extension of this scheme to odd-mass nuclei is a long-standing challenge. We present for the first time such an extension, where the generator coordinate space is built from self-consistently blocked one-quasiparticle HFB states. One of the key points for this success is that the same Skyrme interaction is used for the mean-field and the pairing channels, thus avoiding problems related to the violation of the Pauli principle. An application to ^{25}Mg illustrates the power of our method, as agreement with experiment is obtained for the spectrum, electromagnetic moments, and transition strengths, for both positive and negative parity states and without the necessity for effective charges or effective moments. Although the effective interaction still requires improvement, our study opens the way to systematically describe odd-A nuclei throughout the nuclear chart.

Working with Hamiltonians from chiral effective field theory, we develop a novel framework for describing arbitrary deformed medium-mass nuclei by combining the in-medium similarity renormalization group with the generator coordinate method. The approach leverages the ability of the first method to capture dynamic correlations and the second to include collective correlations without violating symmetries. We use our scheme to compute the matrix element that governs the neutrinoless double beta decay of 48 Ca to 48 Ti, and find it to have the value 0.61, near or below the predictions of most phenomenological methods. The result opens the door to ab initio calculations of the matrix elements for the decay of heavier nuclei such as 76 Ge, 130 Te, and 136 Xe.