Quantum Fisher Information and multipartite entanglement in spin-1 chains

TL;DR

This paper investigates the use of Quantum Fisher Information in spin-1 chains to identify multipartite entanglement and topological phases, employing numerical methods like DMRG and tensor networks.

Contribution

It demonstrates how QFI scaling of non-local observables characterizes phase diagrams and topological phases in spin-1 models, including critical behavior analysis.

Findings

QFI scales maximally in topological phases

QFI scaling characterizes phase diagrams

Critical phase analysis recovers scaling dimensions

Abstract

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 non-local observables can be used for characterizing the phase diagrams and, in particular, for studying topological phases, where it scales maximally. Analysing 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.