Interacting antikinks on a diamondback ladder II

Recently introduced ``antikinks'' are spin 1/2 excitations of the Heisenberg antiferromagnet on a sawtooth lattice [1]. The idea is that they mimic spinons of the kagome antiferromagnet. Antikinks are triangles of spins which are not in their ground state. Treating antikinks as free non-interacting particles (a good approximation for the sawtooth chain), their energy was found to be substantially reduced by delocalization [1]. We study antikinks on a ``diamondback'' ladder in which all spins are shared between two triangles. Consequently, in a uniform case the concentration of antikinks becomes 1/4 and they strongly interact, making such a model a much better approximation for the kagome case. We treat these effects perturbatively by allowing different Heisenberg couplings on the up- and downward oriented triangles, the two limiting cases being the sawtooth and uniform diamondback ladder. We find a non-monotonic, power-law decay of induced interactions between the antikinks with their separation. The consequences of these interactions will be discussed in this talk. \\[4pt] [1] Z. Hao and O. Tchernyshyov, Phys. Rev. Lett. \textbf{103}, 187203 (2009)