A second species of spinons in the $S=1/2$ Heisenberg antiferromagnet on kagome

The $S=1/2$ Heisenberg model on kagome can be viewed as an ensemble of spinons, fermionic quasiparticles with $S=1/2$ bound into small, heavy pairs whose binding energy sets the spin gap [1]. The apparent lack of a spin gap in real kagome magnets (e.g. herbertsmithite) may be associated with the Dzyaloshinskii-Moriya (DM) term $\mathbf{D} \cdot (\mathbf{S}_i \times \mathbf{S}_j)$ in the Hamiltonian allowed by lattice symmetry. The DM term suppresses the spin gap and eventually induces long-range magnetic order [2]. A recent study [3] hints at the presence of an intermediate gapless phase without magnetic order. We propose that this phase arises as a result of condensation of a second spinon species (kinks). Here we study the motion of a single kink on the Husimi cactus, the analog of kagome in a hyperbolic plane. The kink is localized in the pure Heisenberg model and becomes mobile when $D \neq 0$. We calculate the one-particle density of states and the bandwidth. [1] Z. Hao and O. Tchernyshyov, Phys. Rev. Lett. \textbf{103,} 187203 (2009). [2] O. C{\'e}pas \textit{et al.}, Phys. Rev. B 78, 140405 (2008). [3] I. Rousochatzakis \textit{et al.}, Phys. Rev. B \textbf{79,} 214415 (2009).