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 strong-disorder renormalization group (SDRG) 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 where the x-type Ising couplings compete with the z-type couplings and the y-type couplings are small but nonzero, the behavior of the spin gap is consistent with a random transverse-field Ising chain, but the flux gap is dominated by the y-type couplings. In the XX limit, while the x- and y-type couplings are locally equal and renormalized simultaneously, the z-type couplings are not renormalized drastically and lead to nonuniversal disorder criticality at low-energy scales. We show that different types of fractionalized degrees of freedom in the disordered Kitaev model can result in different critical behaviors, as long as its fluxes can survive the perturbative treatment.