Four-concurrence in the transverse XY spin-1/2 chain
AbstractWe analyze the entanglement measure C4 for specific mixed states in general and for the ground state of the transverse XY spin-1/2 chain. We find that its factorizing property for pure states does not easily extend to mixed states. For cases where the density matrix is a tensor product, C4 is definitely upper bounded by the product of the corresponding concurrences. In transverse XY chains, we find that for large distances this condition goes conform with the working hypotheses of a factorizing property of density matrices in this limit. Additionally, we find that C4 together with the genuine multipartite negativity makes it impossible to decide—at the present state of knowledge—which type of entanglement prevails in the system. In particular, this is true for all entanglement measures that detect SL-invariant genuine n-partite entanglement for different n. Further measures of SL-invariant genuine multipartite entanglement have to be considered here. C4 is, however, of the same order of magnitude as the genuine multipartite negativity in Phys. Rev. B 89, 134101 (2014)PRBMDO1098-012110.1103/PhysRevB.89.134101 and shows the same functional behavior, which we read as a hint towards the Greenberger-Horne-Zeilinger (GHZ) type of entanglement. Furthermore, we observe an interesting feature in the C4 values that resembles a destructive interference with the underlying concurrence.