Existence of Fermion Zero Modes and Deconfinement of Spinons in Quantum Antiferromagnetism resulting from Algebraic Spin Liquid

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.