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

Abstract

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 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 $${\pi }$$?-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 Neel phase. To gain further insight, the nonanalytic and scaling behaviors of $${\pi }$$?-tangle have also been analyzed in detail.