Quantum Fisher information and multipartite entanglement in spin-1 chains

In this paper, we study the ground-state quantum Fisher information (QFI) in one-dimensional spin-1 models, as witness to multipartite entanglement. The models addressed are the bilinear-biquadratic model, the most general isotropic SU(2)-invariant spin-1 chain, and the XXZ spin-1 chain, both with nearest-neighbor interactions and open boundary conditions. We show that the scaling of the QFI of strictly nonlocal observables can be used for characterizing the phase diagrams and, in particular, for studying topological phases, where it scales maximally. Analyzing its behavior at the critical phases, we are also able to recover the scaling dimensions of the order parameters, both for local and string observables. The numerical results have been obtained by exploiting the density-matrix renormalization-group algorithm and tensor network techniques.