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

The Kitaev model hosts a quantum spin liquid characterized by a variety of unusual features arising from its topological character, including fractionalized excitations. The search for non-Abelian anyons in Kitaev spin liquids is crucial for advancing fault-tolerant topological quantum computation. It is known that spin vacancies in the Kitaev model bind emergent gauge fluxes that become non-Abelian anyons in an infinitesimal magnetic field. In our work, we investigate how this approach for stabilizing non-Abelian anyons extends to a finite magnetic field along the [111] axis. Using large-scale matrix product state-based numerical methods, we demonstrate the robustness of vacancy-bound non-Abelian anyons in a magnetic field for both the ferromagnetic and antiferromagnetic Kitaev models. By applying relevant perturbations as pinning fields and performing systematic extrapolations, we accurately compute the energies of states within distinct topological sectors, allowing us to precisely determine the binding energy. The robustness of vacancy-bound anyons is further validated through the analysis of physical operators, including extended plaquette operators near vacancies and topological loop operators, under varying cylinder widths and boundary conditions.