  We derive the exact ground space of a family of spin-1/2 Heisenberg chains
with uniaxial exchange anisotropy (XXZ) and interactions between nearest and
next-nearest-neighbor spins. The Hamiltonian family, H(Q), is parametrized by a
single variable Q. By using a generalized Jordan-Wigner transformation that
maps spins into anyons, we show that the exact ground states of H(Q) correspond
to a condensation of anyons with statistical phase phi=-4Q. We also provide
matrix-product state representations of some ground states that allow for the
efficient computation of spin-spin correlation functions.
