In recent years the ab initio treatment of the nuclear many-body problem has seen tremendous progress such that the A-body Schrödinger equation can be solved from first principles using realistic nuclear Hamiltonians with a sound link to QCD. However, it is yet unclear (1) how to describe genuine open-shell nuclei from an ab initio perspective and (2) how to overcome the curse of dimensionality in many-body approaches that prevents relaxing many-body approximations. Additionally, the large uncertainties arising from the input Hamiltonian make a direct comparison with experimental observations challenging, requiring extensive interaction benchmarks far away from shell closures and for large mass numbers in the future.
Exploiting symmetry breaking in the many-body expansion enables for addressing nuclear observables in arbitrary open-shell systems. The recently introduced Bogoliubov extension of many-body perturbation theory serves as an example for a computationally light-weighted approach well-suited for benchmarking ground-state energetics along medium-mass isotopic chains . In a complementary way, data pre-processing techniques help resolving the computational bottlenecks one is facing in state-of-the-art many-body implementations. Two particular strategies are discussed: (i) tensor factorization  and (ii) importance truncation . Due to discarding many irrelevant tensor entries the original large-scale problem can be solved in a much smaller selected model space. The combination of novel many-body expansions and innovative tools from applied mathematics allows us for extending the range of ab initio applications and, thus, putting the next generation of nuclear Hamiltonians to a stringent test at low computational cost.
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