Doping a topological quantum spin liquid: slow holes in the Kitaev honeycomb model - Halász, G (2015)
We present a controlled microscopic study of hole dynamics in both a gapped and a gapless quantum spin liquid. Our approach is complementary to previous phenomenological works on lightly doped quantum spin liquids as we introduce mobile holes into the ground state of the exactly solvable Kitaev honeycomb model. In the spatially anisotropic (Abelian) gapped phase of the model, we address the properties of a single hole [its internal degrees of freedom as well as its hopping properties], a pair of holes [their absolute and relative particle statistics as well as their interactions], and the collective state for a finite density of holes. Our main result is that the holes in the doped model possess internal degrees of freedom as they can bind the fractional excitations of the undoped model and that the resulting composite holes with different excitations bound are distinct fractional particles with fundamentally different single-particle properties and different experimental signatures in the multi-particle ground state at finite doping. For example, some hole types are free to hop in two dimensions, while others are confined to hop in one dimension only. Also, distinct hole types have different particle statistics and, in particular, some of them exhibit non-trivial (anyonic) relative statistics. At finite doping, the respective hopping dimensionalities manifest themselves in an electrical conductivity that is either approximately isotropic or extremely anisotropic. In the gapless phase of the model, we consider a single hole and address the possibility of a coherent quasiparticle description. Our main result is that a mobile hole has a finite quasiparticle weight which vanishes in the stationary limit. Although this result is obtained in terms of an approximate variational state, we argue that it is also applicable for the exact ground state of the doped model.