SciPost Phys. 7, 053 (2019) ·
published 22 October 2019

· pdf
We derive some entanglement properties of the ground states of two classes of quantum spin chains described by the Fredkin model, for halfinteger spins, and the Motzkin model, for integer ones. Since the ground states of the two models are known analytically, we can calculate the entanglement entropy, the negativity and the quantum mutual information exactly. We show, in particular, that these systems exhibit longdistance entanglement, namely two disjoint regions of the chains remain entangled even when the separation is sent to infinity, i.e. these systems are not affected by decoherence. This strongly entangled behavior, occurring both for colorful versions of the models (with spin larger than 1/2 or 1, respectively) and for colorless cases (spin 1/2 and 1), is consistent with the violation of the cluster decomposition property. Moreover we show that this behavior involves disjoint segments located both at the edges and in the bulk of the chains.
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in Report on Longdistance entanglement in Motzkin and Fredkin spin chains