Various quantum measures and quantum phase transition within one-dimensional anisotropic spin-1/2 Heisenberg XXZ model

In this work, we investigate the dynamical properties of various quantum measures (quantum coherence and correlations) to estimate the system evolution under spin-1/2 Heisenberg XXZ model by utilizing quantum renormalization-group method. It has been shown that quantum coherence and correlations can be used to effectively detect a quantum critical point associated with a quantum phase transition (QPT) after several iterations of renormalization. Additionally, we obtain that the dynamical behavior of l1 norm of coherence is in agreement with that of concurrence and double trace distance discord. Interestingly, Bell-CHSH inequality cannot be violated with increasing of the spin system size N. That is, the block-block Bell nonlocality cannot be revealed. Moreover, we reveal some quantitative relations between quantum coherence and some quantum correlations, and thus the l1 norm of coherence is more conducive for probing the QPT at the critical point within the composite systems. Further, the scaling behaviors and nonanalytic phenomenon of the l1 norm of coherence and quantum discord are discussed in detail.