  We present a numerical method based on real-space renormalization that
outputs the exact ground space of "frustration-free" Hamiltonians. The
complexity of our method is polynomial in the degeneracy of the ground spaces
of the Hamiltonians involved in the renormalization steps. We apply the method
to obtain the full ground spaces of two spin systems. The first system is a
spin-1/2 Heisenberg model with four-spin cyclic-exchange interactions defined
on a square lattice. In this case, we study finite lattices of up to 160 spins
and find a triplet ground state that differs from the singlet ground states
obtained in C.D. Batista and S. Trugman, Phys. Rev. Lett. 93, 217202 (2004). We
characterize such a triplet state as consisting of a triplon that propagates in
a background of fluctuating singlet dimers. The second system is a family of
spin-1/2 Heisenberg chains with uniaxial exchange anisotropy and next-nearest
neighbor interactions. In this case, the method finds a ground-space degeneracy
that scales quadratically with the system size and outputs the full ground
space efficiently. Our method can substantially outperform methods based on
exact diagonalization and is more efficient than other renormalization methods
when the ground-space degeneracy is large.
