  The quantum phase transition in an atom-molecule conversion system with
atomic hopping between different hyperfine states is studied. In mean field
approximation, we give the phase diagram whose phase boundary only depends on
the atomic hopping strength and the atom-molecule energy detuning but not on
the atomic interaction. Such a phase boundary is further confirmed by the
fidelity of the ground state and the energy gap between the first-excited state
and the ground one. In comparison to mean field approximation, we also study
the quantum phase transition in full quantum method, where the phase boundary
can be affected by the particle number of the system. Whereas, with the help of
finite-size scaling behaviors of energy gap, fidelity susceptibility and the
first-order derivative of entanglement entropy, we show that one can obtain the
same phase boundary by the MFA and full quantum methods in the limit of
$N\rightarrow \infty$. Additionally, our results show that the quantum phase
transition can happens at the critical value of the atomic hopping strength
even if the atom-molecule energy detuning is fixed on a certain value, which
provides one a new way to control the quantum phase transition.
