  We use entanglement to investigate the transition from vortex liquid phase to
vortex lattice phase in weakly interacting rotating Bose-Einstein condensate
(BEC). Ground state entanglement spectrum is analyzed to distinguish these two
different phases. For the torus geometry, the low-lying part of ground state
entanglement spectrum, as well as the behavior of its lowest level change
clearly when the transition occurs. For the sphere geometry, the disappearance
of entanglement gap in the conformal limit (CL) can indicate this transition.
We also show that the decrease of entanglement between particles can be
regarded as a signal of the transition.
