  The extension of ab initio quantum many-body theory to higher accuracy and
larger systems is intrinsically limited by the handling of large data objects
in form of wave-function expansions and/or many-body operators. In this work we
present matrix factorization techniques as a systematically improvable and
robust tool to significantly reduce the computational cost in many-body
applications at the price of introducing a moderate decomposition error. We
demonstrate the power of this approach for the nuclear two-body systems, for
many-body perturbation theory calculations of symmetric nuclear matter, and for
non-perturbative in-medium similarity renormalization group simulations of
finite nuclei. Establishing low-rank expansions of chiral nuclear interactions
offers possibilities to reformulate many-body methods in ways that take
advantage of tensor factorization strategies.
