  The honeycomb Kitaev spin model provides a quantum spin liquid in the ground
state, where the spin excitations are fractionalized into itinerant and
localized Majorana fermions; the former spectrum has a broad continuum ranging
up to a high energy, while the latter has a sharp peak at a low energy. Despite
tremendous efforts, it remains elusive to clearly identify these distinct
Majorana excitations in experiments. Here we show their manifestation in the
time evolution after quenching the magnetic field, by using the time-dependent
Majorana mean-field theory for both the ferromagnetic and antiferromagnetic
Kitaev models. We find that the transient spin dynamics from the quantum spin
liquid states is qualitatively different from the conventional spin precessions
by the quench from the high-field forced-ferromagnetic state. We obtain
peculiar time evolutions with distinct time scales, i.e., short-time decay of
high-energy components associated with the itinerant Majorana excitations, and
long-lived excitations at a low energy by the localized ones. These peculiar
behaviors are caused by the energy transfer between the two Majorana
quasiparticles after the field quench. Moreover, we find that the Majorana
semimetal with the point nodes in equilibrium turns into a Majorana metal with
the transient "Fermi surfaces" by the energy transfer. In particular, for the
quench from the intermediate-field quantum spin liquid in the antiferromagnetic
Kitaev model, the Fermi surfaces change their topology in the time evolution,
which is regarded as a dynamical version of the Majorana "Lifshitz transition".
Our results unveil that the real-time dynamics provides another route to not
only the identification of the fractional Majorana excitations in candidate
materials of Kitaev magnets but also unprecedented quantum phases that cannot
be stabilized as the equilibrium states.
