## SciPost Submission Page

# 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 |

### Abstract

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.