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Long-distance entanglement in Motzkin and Fredkin spin chains

by Luca Dell'Anna

Submission summary

As Contributors: Luca Dell'Anna
Preprint link: scipost_201905_00002v1
Date submitted: 2019-05-12
Submitted by: Dell'Anna, Luca
Submitted to: SciPost Physics
Domain(s): Theoretical
Subject area: Quantum Physics


We derive some entanglement properties of the ground states of two classes of quantum spin chains described by the Fredkin model for half-integer 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 long-distance 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 is consistent with the violation of the cluster decomposition property occurring in the case of colorful versions of the models (with spin larger than 1/2 or 1, respectively), but is also verified for colorless cases (spin 1/2 and 1). Moreover we show that this behavior involves disjoint segments located both at the edges and in the bulk of the chains.

Current status:
Editor-in-charge assigned

Submission & Refereeing History

Submission scipost_201905_00002v1 on 12 May 2019

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