  We identify a large class of quantum many-body systems that can be solved
exactly: natural frustration-free spin-1/2 nearest-neighbor Hamiltonians on
arbitrary lattices. We show that the entire ground state manifold of such
models can be found exactly by a tensor network of isometries acting on a space
locally isomorphic to the symmetric subspace. Thus, for this wide class of
models real-space renormalization can be made exact. Our findings also imply
that every such frustration-free spin model satisfies an area law for the
entanglement entropy of the ground state, establishing a novel large class of
models for which an area law is known. Finally, we show that our approach gives
rise to an ansatz class useful for the simulation of almost frustration-free
models in a simple fashion, outperforming mean field theory.
