Level crossing and quantum phase transition of the XY model

The ground state of a one-dimensional spin-1/2 chain with periodical boundary condition in the Heisenberg XY model is investigated. We consider the spatial correlation and concurrence between any nearest-neighbor pair of spins under the conditions of different coupling strength, anisotropic parameter and magnitude of a transverse field. Quantum phase transitions due to the competition between coupling and alignment which cause the abrupt changes of the correlation and concurrence are observed. The transition are direct results of the level crossing.