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The characterization of an infinite-order quantum phase transition (QPT) byentanglement measures is analyzed. To this aim, we consider two closely relatedsolvable spin-1/2 chains, namely, the Ashkin-Teller and the staggered XXZmodels. These systems display a distinct pattern of eigenstates but exhibit thesame thermodynamics, i.e. the same energy spectrum. By performing exactdiagonalization, we investigate the behavior of pairwise and block entanglementin the ground state of both models. In contrast with the XXZ chain, we showthat pairwise entanglement fails in the characterization of the infinite-orderQPT in the Ashkin-Teller model, although it can be achieved by analyzing thedistance of the pair state from the separability boundary. Concerning blockentanglement, we show that both XXZ and Ashkin-Teller models exhibit identicalvon Neumann entropies as long as a suitable choice of blocks is performed.Entanglement entropy is then shown to be able to identify the quantum phasediagram, even though its local extremes (either maximum or minimum) may alsoappear in the absence of any infinite-order QPT.

Entanglement and local extremes at an infinite-order quantum phase transition