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Long-distance entanglement in Motzkin and Fredkin spin chains
by Luca Dell'Anna
- Published as SciPost Phys. 7, 053 (2019)
|As Contributors:||Luca Dell'Anna|
|Date submitted:||2019-09-23 02:00|
|Submitted by:||Dell'Anna, Luca|
|Submitted to:||SciPost 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, 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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Published as SciPost Phys. 7, 053 (2019)
Author comments upon resubmission
hereafter the new version of the paper with the changes made in accordance with the requests of the Referee.
The reply and the changes have been already sent in July.
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The list of changes has been sent already in the reply to the Referee's report in July.
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Reports on this Submission
Anonymous Report 1 on 2019-10-1 Invited Report
I think the manuscript is improved and I am satisfied with the author's changes and responses to my requested changes.
I now recommend publication, however I did find at least one typo that a standard spellcheck would have turned up (bottom of page 7, "Before to proceed ne need to know").