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 mostgeneral isotropic SU(2)-invariant spin-1 chain, and the XXZ spin-1 chain, both with nearest-neighbor interactionsand open boundary conditions. We show that the scaling of the QFI of strictly nonlocal observables canbe used for characterizing the phase diagrams and, in particular, for studying topological phases, where it scalesmaximally. Analyzing its behavior at the critical phases, we are also able to recover the scaling dimensions of theorder parameters, both for local and string observables. The numerical results have been obtained by exploitingthe density-matrix renormalization-group algorithm and tensor network techniques.