Fractionalization in an easy-axis Kagome antiferromagnet

We study an antiferromagnetic spin-$1/2$ model with up to third nearest-neighbor couplings on the Kagome lattice in the easy-axis limit, and show that its low-energy dynamics are governed by a four-site $\mathrm{XY}$ ring exchange Hamiltonian. Simple “vortex pairing” arguments suggest that the model sustains a novel fractionalized phase, which we confirm by exactly solving a modification of the Hamiltonian including a further four-site interaction.In this limit, the system is a featureless “spin liquid,” with gaps to all excitations, in particular: deconfined $S^z=1/2\mathrm{}$ bosonic “spinons” and Ising vortices or “visons.” We use an Ising duality transformation to express vison correlators as nonlocal strings in terms of the spin operators, and calculate the string correlators using the ground state wave function of the modified Hamiltonian. Remarkably, this wave function is exactly given by a kind of Gutzwiller projection of an $\mathrm{XY}$ ferromagnet.Finally, we show that the deconfined spin-liquid state persists over a finite range as the additional four-spin interaction is reduced, and study the effect of this reduction on the dynamics of spinons and visons.