Long-distance entanglement in Motzkin and Fredkin spin chains
arXiv:1904.05205 · doi:10.21468/SciPostPhys.7.4.053
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, 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.
36 pages, 13 figures
References in corpus (8)
- Area laws in quantum systems: mutual information and correlations
- On the quantum, classical and total amount of correlations in a quantum state
- Entanglement negativity in quantum field theory
- Lieb-Robinson Bounds and the Exponential Clustering Theorem
- Entanglement entropy of two disjoint intervals in conformal field theory II
- Long-distance entanglement in spin systems
- Gapless quantum spin chains: multiple dynamics and conformal wavefunctions
- Renyi entropy of highly entangled spin chains
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