# Unveiling $${\pi }$$ π -tangle and quantum phase transition in the one-dimensional anisotropic XY model

Unveiling $${\pi }$$ π -tangle and quantum phase transition in the one-dimensional... In this paper, the relationship between $${\pi }$$ π -tangle and quantum phase transition (QPT) is investigated by employing the quantum renormalization-group method in the one-dimensional anisotropic XY model. The results show that all the 1-tangles increase firstly and then decrease with the anisotropy parameter $$\gamma$$ γ increasing, and the Coffman–Kundu–Wootters monogamy inequality is always tenable for this system. The entanglement’s status of subsystems depends on its site position, and this proposition can be generalized to a multipartite system. Meanwhile, with the increasing of the size of the system, the $${\pi }$$ π -tangle decreases slowly and tends to a fixed value finally. Additionally, it exhibits a QPT and a maximum value for the next-nearest-neighbor entanglement at the critical point in our model, which is different from the case of two-body system. After several iterations of the renormalization, the quantum entanglement measure can develop two saturated values, which are associated with two different phases: spin-fluid phase and the Néel phase. To gain further insight, the nonanalytic and scaling behaviors of $${\pi }$$ π -tangle have also been analyzed in detail. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Unveiling $${\pi }$$ π -tangle and quantum phase transition in the one-dimensional anisotropic XY model

, Volume 14 (6) – Apr 8, 2015
12 pages

/lp/springer_journal/unveiling-pi-tangle-and-quantum-phase-transition-in-the-one-uQj4Ff6Wf5
Publisher
Springer US
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-015-0982-4
Publisher site
See Article on Publisher Site

### Abstract

In this paper, the relationship between $${\pi }$$ π -tangle and quantum phase transition (QPT) is investigated by employing the quantum renormalization-group method in the one-dimensional anisotropic XY model. The results show that all the 1-tangles increase firstly and then decrease with the anisotropy parameter $$\gamma$$ γ increasing, and the Coffman–Kundu–Wootters monogamy inequality is always tenable for this system. The entanglement’s status of subsystems depends on its site position, and this proposition can be generalized to a multipartite system. Meanwhile, with the increasing of the size of the system, the $${\pi }$$ π -tangle decreases slowly and tends to a fixed value finally. Additionally, it exhibits a QPT and a maximum value for the next-nearest-neighbor entanglement at the critical point in our model, which is different from the case of two-body system. After several iterations of the renormalization, the quantum entanglement measure can develop two saturated values, which are associated with two different phases: spin-fluid phase and the Néel phase. To gain further insight, the nonanalytic and scaling behaviors of $${\pi }$$ π -tangle have also been analyzed in detail.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Apr 8, 2015

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