Concurrence in collective models

We review the entanglement properties in collective models and their relationship with quantum phase transitions. Focusing on the concurrence, which characterizes the two-spin entanglement, we show that for first-order transitions, this quantity is singular but continuous at the transition point, contrary to the common belief. We also propose a conjecture for the concurrence of arbitrary symmetric states which connects it with a recently proposed criterion for bipartite entanglement.