Creation and Manipulation of Anyons in the Kitaev Model

We analyze the effect of local spin operators in the Kitaev model on the honeycomb lattice. We show, in perturbation around the isolated-dimer limit, that they create Abelian anyons together with fermionic excitations which are likely to play a role in experiments. We derive the explicit form of the operators creating and moving Abelian anyons without creating fermions and show that it involves multispin operations. Finally, the important experimental constraints stemming from our results are discussed.

Figure 1

Mapping of the honeycomb (brick-wall) lattice (a) onto an effective square lattice (b) with unit basis vectors ${\mathit{n}}_1$ and ${\mathit{n}}_2$. The numbering of the sites of a plaquette $p$ is shown in both cases.

Figure 2

Behavior of the spectral weights $I_n^z$ (left) and $I_n^y$ (right) for fermion numbers $n=0$, 2, 4, as a function of the coupling $J=J_x=J_y$ for $J_z=1/2$. Gray plaquettes in the insets $p_1^{z(y)}$ and $p_2^{z(y)}$ show where anyons are created under the action of ${\tau }_{\mathit{i}}^z$ (left) and ${\tau }_{\mathit{i}}^y$ (right).

Figure 3

Action, in the vortex-free sector, of the string operator $S={\sigma }_{\mathit{i},•3}^z{\sigma }_{\mathit{i},•2}^z{\sigma }_{\mathit{i},•1}^z$. Each operator flips the two plaquettes adjacent to the $z$ dimer it is attached to but also creates fermionic excitations (not shown).