  The Kitaev model on a honeycomb lattice with bond-dependent Ising
interactions offers an exactly solvable model of a quantum spin liquid (QSL)
with gapped $Z_2$ fluxes and gapless linearly dispersing Majorana fermions in
the isotropic limit ($K_x=K_y=K_z$). We explore the phase diagram along two
axes, an external magnetic field, $h$, applied out-of-plane of the honeycomb,
and anisotropic interactions, $K_z$ larger than the other two. For $K_z/K\gg 2$
and $h=0$, the matter Majorana fermions have the largest gap, and the system is
described by a gapped $Z_2$ Toric code in which the $Z_2$ fluxes form the low
energy bosonic Ising electric (e) and magnetic (m) charges along with their
fermionic bound state $\epsilon=e\times m$. In this regime, we find that a
small out-of-plane magnetic field creates $\epsilon$ fermions that disperse in
fixed one-dimensional directions before the transition to a valence bond solid
phase, providing a direct dynamical signature of low energy $Z_2$ Abelian flux
excitations separated from the Majorana sector. At lower $K_z$ in the center of
the Abelian phase, in a regime we dub the primordial fractionalized (PF)
regime, the field generates a hybridization between the $\epsilon$ fermions and
the Majorana matter fermions, resulting in a $\psi$ fermion. All the other
phases in the field-anisotropy plane are naturally obtained from this
primordial soup. We show that in the $Z_2$ Abelian phase, including the PF
regime, the dynamical structure factors of local spin flip operators reveal
distinct peaks that can be identified as arising from different anyonic
excitations. We present in detail their signatures in energy and momentum and
propose their identification by inelastic light scattering or inelastic
polarized neutron scattering as ``smoking gun" signatures of fractionalization
in the QSL phase.
