  The fractionalization of microscopic degrees of freedom is a remarkable
manifestation of strong interactions in quantum many-body systems. Analytical
studies of this phenomenon are primarily based on two distinct frameworks:
field theories of partons and emergent gauge fields, or coupled arrays of
one-dimensional quantum wires. We unify these approaches for two-dimensional
spin systems. Via exact manipulations, we demonstrate how parton gauge theories
arise in microscopic wire arrays and explicitly relate spin operators to
emergent quasiparticles and gauge-field monopoles. This correspondence allows
us to compute physical correlation functions within both formulations and leads
to a straightforward algorithm for constructing parent Hamiltonians for a wide
range of exotic phases. We exemplify this technique for several chiral and
non-chiral quantum spin liquids.
