  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.
