  In this paper a geometric phase of the Kitaev honeycomb model is derived and
proposed to characterize the topological quantum phase transition. The
simultaneous rotation of two spins is crucial to generate the geometric phase
for the multi-spin in a unit-cell unlike the one-spin case. It is found that
the ground-state geometric phase, which is non-analytic at the critical points,
possesses zigzagging behavior in the gapless $B$ phase of non-Abelian anyon
excitations, but is a smooth function in the gapped $A$ phase. Furthermore, the
finite-size scaling behavior of the non-analytic geometric phase along with its
first- and second-order partial derivatives in the vicinity of critical points
is shown to exhibit the universality. The divergent second-order derivative of
geometric phase in the thermodynamic limit indicates the typical second-order
phase transition and thus the topological quantum phase transition can be well
described in terms of the geometric-phase.
