In order to quantify entanglement between two parts of a quantum system, one
of the most used estimator is the Von Neumann entropy. Unfortunately, computing
this quantity for large interacting quantum spin systems remains an open issue.
Faced with this difficulty, other estimators have been proposed to measure
entanglement efficiently, mostly by using simulations in the valence-bond
basis. We review the different proposals and try to clarify the connections
between their geometric definitions and proper observables. We illustrate this
analysis with new results of entanglement properties of spin 1 chains.Comment: Proceedings of StatPhys 24 satellite conference in Hanoi; submitted
for a special issue of Modern Physics Letters
