Quantum Fisher Information for bilinear-biquadratic model

In this thesis we show how the Quantum Fisher Information is effective to detect the multipartite structure of entanglement in the topological phases for a certain spin-1 system: the bilinear-biquadratic model. We provide the analytical form of QFI by using string operators. In particular we are interested in the shape of the density of QFI (f) because it provides directly a measure of entanglement for the ground state of a system. Indeed, performing numerical calculations moving from the Haldane phase to the dimer one, we really find a different behavior of f also in the phase transition point. Furthermore we confirm that valence-bound picture is the exact representation for the ground state of AKLT point where the entanglement is maximum while it can be considered a good approximation for the dimer phase.