  The square-lattice quantum Heisenberg antiferromagnet displays a pronounced
anomaly of unknown origin in its magnetic excitation spectrum. The anomaly
manifests itself only for short wavelength excitations propagating along the
direction connecting nearest neighbors. Using polarized neutron spectroscopy,
we have fully characterized the magnetic fluctuations in the model
metal-organic compound CFTD, revealing an isotropic continuum at the anomaly
indicative of fractional excitations. A theoretical framework based on the
Gutzwiller projection method is developed to explain the origin of the
continuum at the anomaly. This indicates that the anomaly arises from
deconfined fractional spin-1/2 quasiparticle pairs, the 2D analog of 1D
spinons. Away from the anomaly the conventional spin-wave spectrum is recovered
as pairs of fractional quasiparticles bind to form spin-1 magnons. Our results
therefore establish the existence of fractional quasiparticles in the simplest
model two dimensional antiferromagnet even in the absence of frustration.
