  The ground state entanglement of the two-mode Bose-Einstein condensate is
investigated through a quantum phase transition approach. The entanglement
measure is taken as the order parameter and this is a non-local order
parameter, which is different from the conventional order parameter of the Mott
insulator-superfluid phase transitions. For this non-local order parameter,
scaling behavior corresponding to a continuous phase transition is obtained and
a power-law divergence near the critical region follows it. This scaling
behavior of quantum entanglement is analyzed by the finite-size scaling and the
critical exponents are obtained as $\nu = 1.01$ and $\gamma = 0.86$. A close
connection between quantum fluctuations and the phase transition of
entanglement is also obtained.
