Robustness of Vacancy-Bound Non-Abelian Anyons in the Kitaev Model in a Magnetic Field

Non-Abelian anyons in quantum spin liquids (QSLs) provide a promising route to fault-tolerant topological quantum computation. In the exactly solvable 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 simulations, we compute the vacancy-anyon binding energy as a function of magnetic field for both the ferromagnetic and antiferromagnetic Kitaev models. We find that anyon binding remains robust within the entire QSL phase for the ferromagnetic Kitaev model but breaks down already inside this phase for the antiferromagnetic Kitaev model. To compute a binding energy several orders of magnitude below the magnetic energy scale, we introduce both a refined definition and an extrapolation scheme based on carefully tailored perturbations.