  We demonstrate that spin-charge separation can occur in two dimensions and
note its confluence with superconductivity, topology, gauge theory, and
fault-tolerant quantum computation. We construct a microscopic Ising-like model
and, at a special coupling constant value, find its exact ground state as well
as neutral spin 1/2 (spinon), spinless charge e (holon), and $Z_2$ vortex
(vison) states and energies. The fractionalized excitations reflect the
topological order of the ground state which is evinced by its fourfold
degeneracy on the torus -- a degeneracy which is unrelated to translational or
rotational symmetry -- and is described by a $Z_2$ gauge theory. Our model is
related to the quantum dimer model and is a member of a family of
topologically-ordered models, one of which is integrable and realizes the toric
quantum error correction code.
