Local entanglement and quantum phase transition in the Hubbard model

The local entanglement $E_v$ of the one-dimensional Hubbard model is studied on the basis of its Bethe-ansatz solution. The relationship between the local entanglement and the on-site Coulomb interaction $U$ is obtained. Our results show that $E_v$ is an even analytic function of $U$ at half-filling and it reaches a maximum at the critical point U=0. The variation of the local entanglement with the filling factor shows that the ground state with maximal symmetry possesses maximal entanglement. The magnetic field makes the local entanglement to decrease and approach to zero at saturated magnetization. The on-site Coulomb interaction always suppresses the local entanglement.