Stability and Control of Mobile and Defect-Bound Non-Abelian Anyons in the Kitaev Spin Liquid

Non-Abelian anyons in quantum spin liquids (QSLs) provide a promising route to fault-tolerant topological quantum computation. In the Kitaev honeycomb model, such anyons of the QSL state can be bound to nonmagnetic spin vacancies and endowed with non-Abelian statistics by an infinitesimal magnetic field. Here, we investigate how this approach for stabilizing non-Abelian anyons extends to a finite magnetic field represented by a proper Zeeman term. Through large-scale density-matrix renormalization group (DRMG) simulations, we compute the vacancy-anyon binding energy as a function of magnetic field for both the ferromagnetic (FM) and antiferromagnetic (AFM) Kitaev models. We find that anyon binding remains robust within the entire QSL phase for the FM Kitaev model but breaks down already inside this phase for the AFM Kitaev model. We further investigate a single mobile hole in the gapped phase using controlled perturbation theory and large-scale DMRG, and construct the binding phase diagram as a function of magnetic field strength, dopant hopping amplitude, and the sign of the Kitaev interaction, thereby identifying the parameter regimes in which the dopant binds a non-Abelian anyon. These results quantify the stability of vacancy-induced non-Abelian defects under realistic fields and identify conditions under which mobile charge carriers inherit non-Abelian character, with implications for materials and device designs targeting braiding-based quantum operations.