Detect genuine multipartite entanglement in the one-dimensional transverse-field Ising model

TL;DR

This paper demonstrates that the ground states of the one-dimensional transverse-field Ising model exhibit genuine multipartite entanglement under weak magnetic fields, providing a new method for experimental verification using NMR simulations.

Contribution

It applies Bell-type inequalities to confirm GME in the Ising model's ground states, offering a practical approach for experimental testing.

Findings

Ground states violate Bell-type inequalities under weak magnetic fields

GME is confirmed in the model's ground states with weak magnetic fields

Results suggest feasible experimental tests using NMR simulations

Abstract

Recently Seevinck and Uffink argued that genuine multipartite entanglement (GME) had not been established in the experiments designed to confirm GME. In this paper, we use the Bell-type inequalities introduced by Seevinck and Svetlichny [Phys. Rev. Lett. \textbf{89}, 060401 (2002)] to investigate the GME problem in the one-dimensional transverse-field Ising model. We show explicitly that the ground states of this model violate the inequality when the external transverse magnetic field is weak, which indicate that the ground states in this model with weak magnetic field are fully entangled. Since this model can be simulated with nuclear magnetic resonance, our results provide a fresh approach to experimental test of GME.