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We provide a study of various quantum phase transitions occurring in the XYHeisenberg chain in a transverse magnetic field using the Meyer-Wallach (MW)measure of (global) entanglement. Such a measure, while being readilyevaluated, is a multipartite measure of entanglement as opposed to morecommonly used bipartite measures. Consequently, we obtain analytic expressionof the measure for finite-size systems and show that it can be used to obtaincritical exponents via finite-size scaling with great accuracy for the Isinguniversality class. We also calculate an analytic expression for the isotropic(XX) model and show that global entanglement can precisely identify thelevel-crossing points. The critical exponent for the isotropic transition isobtained exactly from an analytic expression for global entanglement in thethermodynamic limit. Next, the general behavior of the measure is calculated inthe thermodynamic limit considering the important role of symmetries for thislimit. The so-called oscillatory transition in the ferromagnetic regime canonly be characterized by the thermodynamic limit where global entanglement isshown to be zero on the transition curve. Finally, the anisotropic transitionis explored where it is shown that global entanglement exhibits an interestingbehavior in the finite-size limit. In the thermodynamic limit, we show thatglobal entanglement shows a cusp singularity across the Ising and anisotropictransition, while showing non-analytic behavior at the XX multicritical point.It is concluded that global entanglement, despite its relative simplicity, canbe used to identify all the rich structure of the ground-state Heisenbergchain.

Global entanglement and quantum phase transitions in the transverse XY Heisenberg chain