Genuine Multipartite Entanglement in the $XY$ Model

TL;DR

This paper investigates the genuine multipartite entanglement in the XY model, demonstrating its effectiveness in detecting entanglement and characterizing phase transitions, especially where bipartite measures are insufficient.

Contribution

The study introduces a multipartite entanglement witness based on permutation operators that effectively detects entanglement and characterizes phase transitions in the XY model.

Findings

Genuine multipartite entanglement is present for most parameter values.

The multipartite quantity characterizes phase transition and scaling properties.

The method outperforms bipartite measures in certain condensed matter systems.

Abstract

We analyze the $XY$ model characterized by an anisotropy $\gamma$ in an external magnetic field $h$ with respect to its genuine multipartite entanglement content (in the thermodynamic and finite size case). Despite its simplicity we show that the quantity -detecting genuine multipartite entanglement through permutation operators and being a lower bound on measures- witnesses the presence of genuine multipartite entanglement for nearly all values of $\gamma$ and $h$. We further show that the phase transition and scaling properties are fully characterized by this multipartite quantity. Consequently, we provide a useful toolbox for other condensed matter systems, where bipartite entanglement measures are known to fail.