We present a controlled microscopic study of mobile holes in the spatially anisotropic (Abelian) gapped phase of the Kitaev honeycomb model. We address the properties of (i) a single hole (its internal degrees of freedom as well as its hopping properties); (ii) a pair of holes [their (relative) particle statistics and interactions]; and (iii) the collective state for a finite density of holes. We find that each hole in the doped model has an eight-dimensional internal space, characterized by three internal quantum numbers: the first two “fractional” quantum numbers describe the binding to the hole of the fractional excitations (fluxes and fermions) of the undoped model, while the third “spin” quantum number determines the local magnetization around the hole. The fractional quantum numbers also encode fundamentally distinct particle properties, topologically robust against small local perturbations: some holes are free to hop in two dimensions, while others are confined to hop in one dimension only; distinct hole types have different particle statistics, and in particular, some of them exhibit nontrivial (anyonic) relative statistics. These particle properties in turn determine the physical properties of the multihole ground state at finite doping, and we identify two distinct ground states with different hole types that are stable for different model parameters. The respective hopping dimensionalities manifest themselves in an electrical conductivity approximately isotropic in one ground state and extremely anisotropic in the other one. We also compare our microscopic study with related mean-field treatments, and discuss the main discrepancies between the two approaches, which in particular involve the possibility of binding fractional excitations as well as the particle statistics of the holes. On a technical level, we describe the hopping of mobile holes via a quasistationary approach, where effective hopping matrix elements are calculated between ground states with stationary holes at different positions. This approach relies on the fact that the model remains exactly solvable in the presence of stationary holes, and that the motion of sufficiently slow holes does not generate bulk excitations in a gapped phase. When the bare hopping amplitude is much smaller than the energy gap, many of our results, in particular those on the hopping properties and the particle statistics, are exact.

• Received 18 March 2014
• Revised 23 June 2014

DOI:https://doi.org/10.1103/PhysRevB.90.035145