Introduction {#section:Introduction}
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Quantum Phase Transitions {#subsection:QPTs}
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Unlike ordinary phase transitions, quantum phase transitions (QPTs) [@Vojta] take place at a temperature of absolute zero and are consequently driven entirely by quantum fluctuations, rather than thermal ones. Moreover, the long-range, algebraically decaying correlations which are characteristic of critical many-body ground states are due entirely to entanglement. As such, one would expect entanglement measures (see Ref. [@EntMeasures] for an overview) to provide further insight into the fundamental physical underpinnings of QPTs, possibly complementing the conventional condensed-matter approach, which relies mostly on two-point correlation functions.

Indeed, Osterloh and co-workers [@OsterlohEtAl] demonstrated singular and scaling behaviour of a bipartite entanglement measure in the vicinity of the critical point in the one-dimensional XY spin model. On the other hand, this behaviour could be understood entirely from that of the relevant two-point correlation functions as these are sufficient to determine the two-particle reduced density matrices. Furthermore, the entanglement between just two sites is not particularly well suited to capturing the large-scale behaviour of correlations, which becomes all the more relevant in the critical regime. This was recognized in Ref. [@BlockEntIC], where the scaling behaviour of the entanglement between a contiguous *block* of $L$ sites with 