  We investigate the non-Abelian topological chiral spin liquid phase in the
two-dimensional (2D) Kitaev honeycomb model subject to a magnetic field. By
combining density matrix renormalization group (DMRG) and exact diagonalization
(ED) we study the energy spectra, entanglement, topological degeneracy, and
expectation values of Wilson loop operators, allowing for robust
characterization. While the ferromagnetic (FM) Kitaev spin liquid is already
destroyed by a weak magnetic field with Zeeman energy $H_*^\text{FM} \approx
0.02$, the antiferromagnetic (AFM) spin liquid remains robust up to a magnetic
field that is an order of magnitude larger, $H_*^\text{AFM} \approx 0.2$.
Interestingly, for larger fields $H_*^\text{AFM} < H < H_{**}^\text{AFM}$, 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.
