Quantum coherence, uncertainty, nonlocal advantage of quantum coherence as indicators of quantum phase transition in the transverse Ising model

In this paper, we investigate the relation among local quantum coherence, quantum uncertainty, and the nonlocal advantage of quantum coherence based on skew information and quantum phase transition in the transverse Ising model by exploring the quantum renormalization group (QRG) method. The results reveal that the amount of the local quantum uncertainty is equal to the local quantum coherence corresponding to the local observable sigma(z) in the model, which can be generalized to a multipartite system. Moreover, the nonlocal advantage of quantum coherence is investigated, and we found that regardless of the value of the external magnet field and the number of QRG iterations, the quantum coherence of the subsystem was steerable, which is not only suitable for the two sites of the block, but also for the nearest-neighbor blocks in the long-ranged ferromagnetic phase. However, as the system becomes large enough, the quantum coherence of the subsystem is not steerable in the paramagnetic phase. Additionally, the QRG implementation of quantum coherence and uncertainty are effective and feasible to detect the quantum critical points associated with quantum phase transitions. We also make use of the QRG method to analyze the thermodynamic limit of the current model and the emergence of the nonanalytic and scaling behaviors of the nonlocal advantage of quantum coherence.