  By using the variational Monte Carlo method, we study the magnetization
process of the Kitaev honeycomb model in a magnetic field. Our trial
wavefunction is a generalized Bardeen-Cooper-Schrieffer wave function with the
Jastrow correlation factor, which exactly describes the ground state of the
Kitaev model at zero magnetic field using the Jordan-Wigner (JW)
transformation. We find that two phase transitions occur for the
antiferromagnetic Kitaev coupling, while only one phase transition occurs for
the ferromagnetic Kitaev coupling. For the antiferromagnetic Kitaev coupling,
we also find that the topology of the momentum distribution of the JW fermions
changes at the transition point from the Kitaev spin liquid to an intermediate
state. Our numerical results indicate that the intermediate state between the
Kitaev spin liquid and the fully polarized phases stably exists in the bulk
system on two dimensions for the antiferromagnetic Kitaev coupling against
many-body correlations.
