  We investigate the quantum antiferromagnetism arising from algebraic spin
liquid via spontaneous chiral symmetry breaking. We claim that in the
antiferromagnet massive Dirac spinons can appear to make broad continuum
spectrum at high energies in inelastic neutron scattering. The mechanism of
spinon deconfinement results from the existence of fermion zero modes in single
monopole potentials. Neel vectors can make a skyrmion configuration around a
magnetic monopole of compact U(1) gauge fields. Remarkably, in the
monopole-skyrmion composite potential the Dirac fermion is shown to have a zero
mode. The emergence of the fermion zero mode forbids the condensation of
monopoles, resulting in deconfinement of Dirac spinons in the quantum
antiferromagnet.
