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

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