Genuine multipartite entanglement in quantum phase transitions

We demonstrate that the global-entanglement (GE) measure defined by Meyer and Wallach [J. Math. Phys. 43, 4273 (2002)] is maximal at the critical point for the Ising chain in a transverse magnetic field. Our analysis is based on the equivalence of GE to the averaged linear entropy, allowing an understanding of multipartite entanglement (ME) features through a generalization of GE for bipartite blocks of qubits. Moreover, in contrast to GE, the proposed ME measure can distinguish three paradigmatic entangled states: ${\mathrm{GHZ}}_N$ (Greenberger-Horne-Zeilinger), $W_N$, and ${\mathrm{EPR}}^{\otimes N∕2}$. As such the generalized measure can detect a genuine ME and is maximal at the critical point.