Robust non-Abelian spin liquid and a possible intermediate phase in the antiferromagnetic Kitaev model with magnetic field
In this work, we investigate the non-Abelian topological chiral spin-liquid phase in the two-dimensional Kitaev honeycomb model subject to a magnetic field. By combining density matrix renormalization group and exact diagonalization we study the energy spectra, entanglement, topological degeneracy, and expectation values of Wilson loop operators, allowing for a robust characterization. While the ferromagnetic Kitaev spin liquid is already destroyed by a weak magnetic field with Zeeman energy $H^{FM}_\ast ≈ 0.02$, the antiferromagnetic (AFM) spin liquid remains robust up to a magnetic field that is an order of magnitude larger, $H^{AFM}_\ast ≈ 0.2$. Interestingly, for larger fields $H^{AFM}_\ast < H < H^{AFM}_{\ast\ast}$, an intermediate gapless phase is observed, before a second transition to the high-field partially polarized paramagnet. We attribute this rich phase diagram, and the remarkable stability of the chiral topological phase in the AFM Kitaev model, to the interplay of strong spin-orbit coupling and frustration enhanced by the magnetic field. Our findings suggest relevance to recent experiments on RuCl 3 under magnetic fields.