Unveiling \({\pi }\)-tangle and quantum phase transition in the one-dimensional anisotropic XY model
In this paper, the relationship between \({\pi }\)-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 \(\gamma \) increasing, and the CoffmanKunduWootters monogamy inequality is always tenable for this system. The entanglements 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 \({\pi }\)-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 Nel phase. To gain further insight, the nonanalytic and scaling behaviors of \({\pi }\)-tangle have also been analyzed in detail.
\({\pi }\)-tangle quantum phase transition quantum entanglement heisenberg xy model