Renormalization of negativity and quantum phase transition in the spin-1/2 XY chainyy

We apply the quantum renormalization group (QRG) method to study the relationship between entanglement and quantum phase transition in the spin-1/2 XY chain. The tripartite negativity and bipartite negativity are considered as the measurements of entanglement for the block state and its reduced state, and the first derivatives and scaling behaviors of tripartite and bipartite negativity are investigated, respectively. The results show that the unstable fixed point (critical point) and the stable fixed point can be revealed by the evolutions of tripartite and bipartite negativity and are verified by the first derivatives of tripartite and bipartite negativity in the thermodynamic limit. Moreover, the singular behaviors are shown in the first derivatives of tripartite and bipartite negativity, indicating that the second-order phase transition occurs. The renormalized tripartite negativity and bipartite negativity obey the same scaling laws in the vicinity of the quantum phase transition point. Our findings indicate that the QRG implementation of negativity can be also regarded as another description of critical behavior of the XY model.