  We study the dynamics of the Lipkin-Meshkov-Glick (LMG) model with finite
number of spins. In the thermodynamic limit, the ground state of the LMG model
with isotropic Hamiltonian in broken phase breaks to a mean-field ground state
with a certain direction. However, when the spins number $N$ is finite, the
exact ground state is always unique and is not given by a classical mean-field
ground state. Here we prove that for $N$ is large but finite, through a tiny
external perturbation, a localized state which is close to a mean-field ground
state can be prepared, which mimics a spontaneous symmetry breaking (SSB).
Besides, we find the localized in-plane spin polarization oscillates with two
different frequencies $\sim O(1/N)$, and the lifetime of the localized state is
long enough to exhibit this oscillation. We numerically test the analytical
results and find that they agree with each other very well. Finally, we link
the phenomena to quantum time crystals and quasicrystals.
