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Using Bell-inequalities as a tool to explore non-classical physicalbehaviours, in this paper we analyze what one can expect to find in many-bodyquantum physics. Concretely, framing the usual correlation scenarios as aconcrete spin-lattice, we want to know whether or not it is possible to violatea Bell-inequality restricted to this scenario. Using clustering theorems, weare able to show that a large family of quantum many-body systems behave almostlocally, violating Bell-inequalities (if so) only by a non-significant amount.We also provide examples, explain some of our assumptions via counter-examplesand present all the proofs for our theorems. We hope the paper isself-contained.

Bell Non-Locality in Many Body Quantum Systems with Exponential Decay of Correlations