We analyze the $XY$ model characterized by an anisotropy $\gamma$ in an external magnetic field, $h$, with respect to its genuine multipartite entanglement content (in the thermodynamic and finite-size case). Despite its simplicity we show that the quantity—detecting genuine multipartite entanglement through permutation operators and being a lower bound on measures—witnesses the presence of genuine multipartite entanglement for nearly all values of $\gamma$ and $h$. We further show that the phase transition and scaling properties are fully characterized by this multipartite quantity. Consequently, we provide a useful toolbox for other condensed-matter systems, where bipartite entanglement measures are known to fail.

• Received 3 September 2013

DOI:https://doi.org/10.1103/PhysRevA.88.052305