Antiferromagnetic Magnons from Fractionalized Excitations*

We develop an approach to describe antiferromagnetic magnons on a bipartite lattice supporting
the Neel state using fractionalized degrees of freedom typically inherent to quantum spin liquids.
In particular we consider a long-range magnetically ordered state of interacting two-dimensional
quantum spin 1/2 models using the Chern-Simons (CS) fermion representation of interacting spins.
The interaction leads to Cooper instability and pairing of CS fermions, and to CS superconductivity
which spontaneously violates the continuous U(1) symmetry generating a linearly-dispersing gapless
Nambu-Goldstone mode due to phase fluctuations. We evaluate this mode and show that it is in
high-precision agreement with magnons of the corresponding Neel antiferromagnet irrespective to
the lattice symmetry.