Multipartite Entanglement Signature of Quantum Phase Transitions

TL;DR

This paper establishes a connection between multipartite entanglement measures and quantum phase transitions, showing that the generalized global entanglement (GGE) can signal critical points, their order, and define a diverging entanglement length.

Contribution

It introduces a relation linking GGE non-analyticities to quantum phase transitions and demonstrates GGE's effectiveness in characterizing critical phenomena in many-particle systems.

Findings

GGE signals critical point location and transition order

Multipartite entanglement is favored at critical points

Entanglement length diverges at second order QPT, proportional to correlation length

Abstract

We derive a general relation between the non-analyticities of the ground state energy and those of a subclass of the multipartite generalized global entanglement (GGE) measure defined by T. R. de Oliveira et al. [Phys. Rev. A 73, 010305(R) (2006)] for many-particle systems. We show that GGE signals both a critical point location and the order of a quantum phase transition (QPT). We also show that GGE allows us to study the relation between multipartite entanglement and QPTs, suggesting that multipartite but not bipartite entanglement is favored at the critical point. Finally, using GGE we were able, at a second order QPT, to define a diverging entanglement length (EL) in terms of the usual correlation length. We exemplify this with the XY spin-1/2 chain and show that the EL is half the correlation length.