Violation of the Bell inequality in quantum critical random spin-$1/2$ chains

TL;DR

This paper explores how breaking translational symmetry in random critical spin chains affects their entanglement and nonlocality, revealing that randomness alone does not guarantee nonlocal quantum states.

Contribution

It demonstrates that breaking translational invariance is necessary but not sufficient for nonlocality in critical spin chains, and compares nonlocality in random versus translationally invariant models.

Findings

Breaking translational invariance is necessary but not sufficient for nonlocality.

Random chains remain local up to small randomness levels.

Random dimer model differs in nonlocality from translationally invariant chain.

Abstract

We investigate the entanglement and nonlocality properties of two random XX spin-1/2 critical chains, in order to better understand the role of breaking translational invariance to achieve nonlocal states in critical systems. We show that breaking translational invariance is a necessary but not sufficient condition for nonlocality, as the random chains remain in a local ground state up to a small degree of randomness. Furthermore, we demonstrate that the random dimer model does not have the same nonlocality properties of the translationally invariant chain, even though they share the same universality class for a certain range of randomness.