Phases and phase transitions of a perturbed Kekulé-Kitaev model

Abstract

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 Kekul\'e 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 $3D\text{\ensuremath{-}}XY\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ universality class.