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The ground state fidelity per lattice site is shown to be able to detectquantum phase transitions for the Kitaev model on the honeycomb lattice, aprototypical example of quantum lattice systems with topological order. It isfound that, in the thermodynamic limit, the ground state fidelity per latticesite is non-analytic at the phase boundaries: the second-order derivative ofits logarithmic function with respect to a control parameter describing theinteraction between neighboring spins is logarithmically divergent. A finitesize scaling analysis is performed, which allows us to extract the correlationlength critical exponent from the scaling behaviors of the ground statefidelity per lattice site.

Singularities in ground-state fidelity and quantum phase transitions for the Kitaev model