The purity entanglement measure introduced by Los Alamos group a decade ago is reexamined in the light of interesting features. The role played by purity, reaching a real thermodynamic limit, in detecting quantum phase transitions is studied with a different system, the bond-alternating $XY$ model in an external magnetic field. The properties of this system are described as well. By considering the dynamics of the original $XY$ model, we observe that nonergodicity is also grasped by the purity measure, in accordance with other quantum correlation measures that have no common physical or mathematical relation. Adiabaticity is not recovered from the dynamic to the static case, in accordance with one of the consequences of the celebrated Kibble-Zurek mechanism.

• Received 9 October 2015

DOI:https://doi.org/10.1103/PhysRevA.92.062341