Flux-gap Renormalization in the Random Kitaev Spin Ladder

The discovery of Kitaev materials and the fact that disorder is inevitable in real samples call for a better understanding of how quenched randomness modifies the quantum spin liquid phase. To address this problem, as a first step we consider disorder effects on the Kitaev spin ladder, where the bonds on the legs (rungs) are covered by alternating x- and y-type (z-type) Ising couplings. Unlike the Kitaev spin chain, plaquette fluxes as conserved quantities can be defined on the ladder. In this talk we present the strong-disorder renormalization group (SDRG) study of Kitaev spin ladder with random interactions. The low-energy physics can be solved perturbatively through the Schrieffer-Wolff transformation. For small J_y, it is similar to the random transverse-field Ising chain (RTIC) where the fixed-point behavior is controlled by J_x and J_z distributions. However, while the pseudo-spin gap is determined by J_x and J_z, the flux gap distribution has additional dependence on J_y. In the extreme-value statistics, we show that in the off-critical region, the pseudo-spin and flux gaps follow the same Griffiths singularity as in RTIC. On the other hand, while the pseudo-spin gap shows the infinite-disorder fixed point at the critical point, the flux gap reveals a different scaling behavior.