  The nature of quantum correlations in strongly correlated systems has been a
subject of intense research. In particular, it has been realized that
entanglement and quantum discord are present at quantum phase transitions and
able to characterize it. Surprisingly, it has been shown for a number of
different systems that qubit pairwise states, even when highly entangled, do
not violate Bell's inequalities, being in this sense local. Here we show that
such a local character of quantum correlations is in fact general for
translation invariant systems and has its origins in the monogamy trade-off
obeyed by tripartite Bell correlations. We illustrate this result in a quantum
spin chain with a soft breaking of translation symmetry. In addition, we extend
the monogamy inequality to the $N$-qubit scenario, showing that the bound
increases with $N$ and providing examples of its saturation through uniformly
generated random pure states.
