  Recent numerical studies indicate that the antiferromagnetic Kitaev honeycomb
lattice model undergoes a magnetic-field-induced quantum phase transition into
a new spin-liquid phase. This intermediate-field phase has been previously
characterized as a gapless spin liquid. By implementing a recently developed
variational approach based on the exact fractionalized excitations of the
zero-field model, we demonstrate that the field-induced spin liquid is gapped
and belongs to Kitaev's 16-fold way. Specifically, the low-field non-Abelian
liquid with Chern number $C=\pm 1$ transitions into an Abelian liquid with
$C=\pm 4$. The critical field and the field-dependent behaviors of key physical
quantities are in good quantitative agreement with published numerical results.
Furthermore, we derive an effective field theory for the field-induced critical
point which readily explains the ostensibly gapless nature of the
intermediate-field spin liquid.
