Dynamics of quantum coherence and quantum phase transitions in XY spin systems

We provide an analysis on the critical property of quantum coherence in XY spin systems based on the quantum renormalization group theory. We find that the quantum coherence obeys a conservation relation, i.e., the quantum coherence of a three-block state that is the sum of its reduced state coherence. The quantum coherence of the whole block state and its reduced state obey similar scaling properties with identical quantum coherence exponent 0.999. This means that the quantum critical behavior of a system may gam from its reduced state. With the unitary operator approaches, we evaluated the evolutionary characteristics of the large-scale system and illustrate its behavior with different initial states. The result shows that quantum coherence periodically fluctuates over time. The period decreases under the system size increasing.