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

The search for non-Abelian anyons in quantum spin liquids (QSLs) is crucial for advancing fault-tolerant topological quantum computation. In the exactly solvable Kitaev honeycomb model, nonmagnetic spin vacancies are known to bind emergent gauge fluxes of the QSL ground state, which in turn become non-Abelian anyons for an infinitesimal magnetic field. Here, we investigate how this approach for stabilizing non-Abelian anyons at spin vacancies extends to a finite magnetic field represented by a proper Zeeman term. Specifically, we use large-scale density-matrix renormalization group (DMRG) simulations to 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, while the inclusion of the field weakens anyon binding in both cases, there is a pronounced difference in the finite-field behavior; the binding energy remains finite within the entire QSL phase for the FM Kitaev model but approaches zero already inside this phase for the AFM Kitaev model. To reliably compute a very small binding energy that is three orders of magnitude below the magnetic interaction strength, we also introduce a refined definition for the binding energy and an extrapolation scheme for its accurate extraction through exclusively ground-state properties using DMRG.