Perturbing the Kitaev Model

The Kitaev model is a fascinating example of an exactly solvable model displaying a spin-liquid ground state in two dimensions. In real materials, however, deviations from the original Kitaev model are expected to appear. In this talk, I will discuss the fate of Kitaev's spin-liquid in the presence of disorder -- bond defects or vacancies -- and other magnetic couplings. Considering static flux backgrounds, we observe a power-law divergence in the low-energy limit of the density of states with a non-universal exponent. We link this power-law distribution of energy scales to weakly coupled droplets inside the bulk, in an uncanny similarity to the Griffiths phase often present in the vicinity of disordered quantum phase transitions. If time-reversal symmetry is broken, we find that power-law singularities are tied to the destruction of the topological phase of the Kitaev model in the presence of bond disorder alone. There is a transition from this topologically trivial phase with power-law singularities to a topologically non-trivial one for weak to moderate site dilution. Therefore, diluted Kitaev materials can potentially host Kitaev's chiral spin-liquid phase.