Topological Transitions and the Spectral Function in the Kitaev-Ising Honeycomb Model

α-RuCl₃ and other materials with Kitaev spin interactions are thought to be proximate to spin liquid phases although they exhibit magnetic order under normal conditions. An important question is thus what features in the spectral function seen in neutron and THz spectroscopy can be understood as precursors of the nearby spin liquid. We address this question by using a simplified model: a strongly-anisotropic Kitaev honeycomb model supplemented by Ising interactions. In certain limits this model is exactly solvable and shows a topological transition with reduced dimensionality. Using numerical simulations and perturbation theory we extend our conclusions to the more generic situation.