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

Highlights: • The uncorrelated random model exhibits arbitrarily separated nonlocal spin pairs. • Nonlocality appears only for nearest-neighbors in the random dimer model. • The number of spin pairs in a nonlocal state increases with the degree of randomness. • Breaking translational invariance is not a sufficient condition for nonlocality. • Systems sharing an universality class may not have the same nonlocality properties. - 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.