Entanglement in the quantum HeisenbergXYmodel

We study the entanglement in the quantum Heisenberg $\mathrm{XY}$ model in which the so-called W entangled states can be generated for 3 or 4 qubits. By the concept of concurrence, we study the entanglement in the time evolution of the $\mathrm{XY}$ model. We investigate the thermal entanglement in the two-qubit isotropic $\mathrm{XY}$ model with a magnetic field and in the anisotropic $\mathrm{XY}$ model, and find that the thermal entanglement exists for both ferromagnetic and antiferromagnetic cases. Some evidences of the quantum phase transition also appear in these simple models.