Zero-energy states and fragmentation of spin in the easy-plane antiferromagnet on a honeycomb lattice

The core of the vortex in the Neel order parameter for an easy-plane antiferromagnet on a honeycomb lattice is demonstrated to bind two zero-energy states. Remarkably, a single electron occupying this midgap band has its spin fragmented between the two sublattices: Whereas it yields a vanishing total magnetization, it shows a finite Neel order, orthogonal to the one of the assumed background. The requisite easy-plane anisotropy may be introduced by a magnetic field parallel to the graphene layer, for example. The results are relevant for spin-1/2 fermions on the graphene's or optical honeycomb lattice, in the strongly interacting regime.