Phases and phase transitions of a perturbed Kekule-Kitaev model

We study the quantum-spin-liquid phase in a variant of the Kitaev model where the bonds of the honeycomb lattice are distributed in a Kekule pattern. The system supports gapped and gapless Z(2) quantum spin liquids with interesting differences from the original Kitaev model, the most notable being a gapped Z(2) spin liquid on a kagome lattice. Perturbing the exactly solvable model with antiferromagnetic Heisenberg perturbations, we find a magnetically ordered phase stabilized by a quantum "order by disorder" mechanism, as well as an exotic continuous quantum phase transition between the topological spin liquid and this magnetically ordered phase. Using a combination of field theory and Monte Carlo simulations, we find that the transition likely belongs to the 3D-XY x Z(2) universality class.