Confinement transition in a Kitaev-like honeycomb model with bond anisotropy

The honeycomb $K-\Gamma$ model is known to have both deconfined spin liquid and confined phases. We study here a confinement transition between the Kitaev spin liquid and a dimerized phase in the limit of strong bond anisotropy. By partially projecting out Majorana states we are able to map the model onto a model of weakly coupled Ising chains in a transverse field. Within this mapping the ordered Ising phase corresponds to the condensation of $Z_2$ fluxes, or confinement. Our results may improve our understanding of the extensively studied spin liquid candidate material $\alpha$-RuCl$_3$, where $K-\Gamma$ interactions are dominant.