SDRG Study of Random Kitaev Chains and Ladders

Recent years have seen a vigorous experimental research campaign on identifying candidate materials for quantum spin liquids (QSL) -- topological states of matter with long-range entanglement and the absence of any broken symmetries. Since some level of disorder in various forms is inevitable in real materials, the effect of quenched disorder in QSLs has arisen a lot of attention. Of specific interest is the role of disorder in the potential Kitaev QSL materials. Here we present a study of random spin-1/2 chain and ladder with bond-directional Kitaev-like interactions. The Kitaev chain consists of alternating 'xx' and 'yy' Ising interactions. By applying the strong-disorder renormalization group (SDRG) on the random Kitaev chain, we demonstrate the presence of infinite-disorder fixed point and quantum Griffiths phase in the low-energy limit. In the Kitaev ladder, chains with alternating 'xx' and 'yy' bonds are connected by the 'zz' Ising interactions on the rungs. We show that the critical properties of the random Kitaev ladder are controlled by the flux operators which are included in the decimation procedure. As a result, local flux gaps get renormalized during SDRG and the low-energy phase contains finite density of fluxes entangled with renormalized spin clusters.