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Long-distance entanglement in Motzkin and Fredkin spin chains

by Luca Dell'Anna

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Submission summary

Authors (as registered SciPost users): Luca Dell'Anna
Submission information
Preprint Link: scipost_201905_00002v2  (pdf)
Date accepted: 2019-10-04
Date submitted: 2019-09-23 02:00
Submitted by: Dell'Anna, Luca
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


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.

Author comments upon resubmission

Dear Editor,
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.

List of changes

The list of changes has been sent already in the reply to the Referee's report in July.

Published as SciPost Phys. 7, 053 (2019)

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").

  • validity: high
  • significance: ok
  • originality: good
  • clarity: good
  • formatting: good
  • grammar: acceptable

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Anonymous on 2019-09-23  [id 608]


The paper is the same as posted in arXiv with the version 1904.05205v3