Entanglement and quantum phase transitions in quantum mixed spin chains

The ground entanglement and thermal entanglement in quantum mixed spin chains consisting of two integer spins 1/2 arrayed 1/2-1/2-1-1 in a unit cell with antiferromagnetic nearest-neighbor couplings J(1) (J(2)) between the spins of equal (different) magnitudes are investigated by employing the logarithmic negativity as entanglement measure. The ground entanglement transition found here is closely related to the valence-bond-solid phase transition, and the thermal entanglement near the critical point is calculated and it is shown that two distinct behaviors exist in the nearest-neighbor same kind of spins and different kind of spins, respectively.