Characterization of topological states via dual multipartite entanglement

TL;DR

This paper shows that multipartite entanglement, measured via quantum Fisher information, can effectively characterize one-dimensional symmetry-protected topological phases, including complex topological states with high winding numbers.

Contribution

It introduces a novel method using dual multipartite entanglement and quantum Fisher information to identify topological phases in the extended Kitaev chain.

Findings

Topological phases with high winding numbers are detected by the scaling of quantum Fisher information.

Dual multipartite entanglement provides richer information than bipartite entanglement.

Method can be generalized to other models like the Kitaev honeycomb model.

Abstract

We demonstrate that multipartite entanglement is able to characterize one-dimensional symmetry-protected topological order, which is witnessed by the scaling behavior of the quantum Fisher information of the ground state with respect to the spin operators defined in the dual lattice. We investigate an extended Kitaev chain with a $\mathbf{Z}$ symmetry identified equivalently by winding numbers and paired Majorana zero modes at each end. The topological phases with high winding numbers are detected by the scaling coefficient of the quantum Fisher information density with respect to generators in different dual lattices. Containing richer properties and more complex structures than bipartite entanglement, the dual multipartite entanglement of the topological state has promising applications in robust quantum computation and quantum metrology, and can be generalized to identify topological order in the Kitaev honeycomb model.