Bell inequalities and entanglement at quantum phase transition in the XXZ Model

TL;DR

This paper demonstrates that Bell inequalities can detect quantum phase transitions in the XXZ model, including transitions not identifiable by entanglement measures, highlighting the nuanced relationship between nonlocality and entanglement.

Contribution

It shows that Bell inequalities can signal various quantum phase transitions in the XXZ model, even when bipartite entanglement does not violate these inequalities.

Findings

Bell inequalities detect first-order and Kosterlitz-Thouless transitions.

Nearest-neighbor entanglement does not violate Bell inequalities.

Bell inequalities reveal transitions beyond bipartite entanglement signals.

Abstract

Entanglement and violation of Bell inequalities are aspects of quantum nonlocality that have been often confused in the past. It is now known that this equivalence is only true for pure states. Even though almost all the studies of quantum correlations at quantum phase transitions deal only with entanglement, we here argue that Bell inequalities can also reveal a general quantum phase transition. This is also shown for a particular case of two spin-1/2 particles in an infinite one-dimensional chain described by the XXZ model. In this case, the Bell inequality is able to signal not only the first-order phase transition, but also the infinite-order Kosterlitz-Thouless quantum phase transition, which cannot be revealed either by the energy of the system nor by the bipartite entanglement. We also show that although the nearest-neighbor spins are entangled, they, unexpectedly, never violate the Bell inequality. This indicates that the type of entanglement which is relevant for quantum phase transition is not trivial, i.e., it cannot be revealed by the Bell inequality.