# Multipartite entanglement in topological quantum phases

## TL;DR

This paper demonstrates how multipartite entanglement, quantified via quantum Fisher information, characterizes topological phases and phase transitions in the Kitaev chain, revealing divergence patterns even without energy gap closing.

## Contribution

It introduces a method to detect topological phases and transitions through multipartite entanglement scaling, applicable to models with variable-range pairing.

## Key findings

- Finite winding number phases show power-law divergence in entanglement scaling.
- Quantum phase transitions are marked by divergence of Fisher information derivative.
- Entanglement signatures persist even when the energy gap does not close.

## Abstract

We witness multipartite entanglement in the Kitaev chain -- a benchmark model of one dimensional topological insulator -- also with variable-range pairing, using the quantum Fisher information. Phases having a finite winding number, both for short- and long-range pairing, are characterized by a power-law diverging finite-size scaling of multipartite entanglement. Moreover the occurring quantum phase transitions are sharply marked by the divergence of the derivative of the quantum Fisher information, even in the absence of a closing energy gap.