  We investigate the relation between Bell function values (BFV) of the reduced
density matrix and the topological quantum phase transitions in the
Kitaev-Castelnovo-Chamon model. % [Phys. Rev. B \textbf{77}, %054433 (2008)].
We find that the first order derivative of BFV exhibits singular behavior at
the critical point and we propose that it can serve as a good and convenient
marker for the transition point. More interestingly, the value of the critical
point can be analytically obtained in this approach. Since the BFV serves as a
measure of nonlocality when it is greater than the classical bound of the
correlation functions, our work has established a link between quantum
nonlocality and phase transitions.

Quantum Physics