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At the core of every frustrated system, one can identify the existence offrustrated rings that are usually interpreted in terms of single--particlephysics. We check this point of view through a careful analysis of theentanglement entropy of both models that admit an exact single--particledecomposition of their Hilbert space due to integrability and those for whichthe latter is supposed to hold only as a low energy approximation. Inparticular, we study generic spin chains made by an odd number of sites withshort-range antiferromagnetic interactions and periodic boundary conditions,thus characterized by a weak, i.e. nonextensive, frustration. While fordistances of the order of the correlation length the phenomenology of thesechains is similar to that of the non-frustrated cases, we find that correlationfunctions involving a number of sites scaling like the system size followdifferent rules. We quantify the long-range correlations through the vonNeumann entanglement entropy, finding that indeed it violates the area law,while not diverging with the system size. This behavior is well fitted by auniversal law that we derive from the conjectured single--particle picture.

The Frustration of being Odd: Universal Area Law violation in local systems