  We present a systematic downfolding many-body approach for extended systems.
Many-body calculations operate on a simpler Hamiltonian which retains
material-specific properties. The Hamiltonian is systematically improvable and
allows one to dial, in principle, between the simplest model and the original
Hamiltonian. As a by-product, pseudopotential errors are essentially eliminated
using a frozen-core treatment. The computational cost of the many-body
calculation is dramatically reduced without sacrificing accuracy. We use the
auxiliary-field quantum Monte Carlo (AFQMC) method to solve the downfolded
Hamiltonian. Excellent accuracy is achieved for a range of solids, including
semiconductors, ionic insulators, and metals. We further test the method by
determining the spin gap in NiO, a challenging prototypical material with
strong electron correlation effects. This approach greatly extends the reach of
general, ab initio many-body calculations in materials.
