  The standard Landau-Ginzburg scenario of phase transition is broken down for
quantum phase transition. It is difficult to find an order parameter to
indicate different phases for quantum fluctuations. Here, we suggest a
topological description of the quantum phase transition for the XY model. The
ground states are identified as a specialized U(1) principal bundle on the base
manifold $S^2$. And then different first Chern numbers of U(1) principal bundle
on the base manifold $S^2$ are associated to each phase of quantum
fluctuations. The particle-hole picture is used to parameterized the ground
states of the XY system. We show that a singularity of the Chern number of the
ground states occurs simultaneously with a quantum phase transition. The Chern
number is a suitable topological order of the quantum phase transition.
