  Elementary excitations in highly entangled states such as quantum spin
liquids may exhibit exotic statistics, different from those obeyed by
fundamental bosons and fermions. Excitations called non-Abelian anyons are
predicted to exist in a Kitaev spin liquid - the ground state of an exactly
solvable model proposed by Kitaev almost a decade ago. A smoking-gun signature
of such non-Abelian anyons, namely a half-integer quantized thermal Hall
conductivity, was recently reported in $\alpha$-RuCl$_3$. While fascinating, a
microscopic theory for this phenomenon in $\alpha$-RuCl$_3$ remains elusive
because the pure Kitaev phase cannot capture these anyons appearing in an
intermediate magnetic field. Here we present a microscopic theory of the Kitaev
spin liquid emerging between the low- and high-field states. Essential to this
result is an antiferromagnetic off-diagonal symmetric interaction that permits
the Kitaev spin liquid to protrude from the pure ferromagnetic Kitaev limit
under a magnetic field. This generic model captures a field-revealed Kitaev
spin liquid, and displays strong anisotropy of field effects. A wide regime of
non-Abelian anyon Kitaev spin liquid is predicted when the magnetic field is
perpendicular to the honeycomb plane.
