  We explore a dynamic signature of quantum phase transition (QPT) in an
isotropic Lipkin-Meshkov-Glick (LMG) model by studying the time evolution of a
central qubit coupled to it. We evaluate exactly the time-dependent purity,
which can be used to measure quantum coherence, of the central qubit. It is
found that distinctly different behaviors of the purity as a function of the
parameter reveal clearly the QPT point in the system. It is also clarified that
the present model is equivalent to an anti Jaynes-Cummings model under certain
conditions.
