Spin- and Flux-gap Renormalization in the Random Kitaev Spin Ladder

We study the Kitaev spin ladder with random couplings by using the real-space renormalization group technique. This model is the minimum model in Kitaev systems that has conserved plaquette fluxes, and its quasi-one-dimensional geometry makes it possible to study the strong-disorder fixed points for both spin- and flux- excitation gaps. In the Ising limit, the behavior of the spin gap is consistent with the familiar random transverse-field Ising chain, but the flux gap is dominated by the y-coupling. In the XX limit, while the x- and y-couplings are renormalized simultaneously, the z-couplings are not renormalized drastically and lead to non-universal disorder criticality at low-energy scales.