Quantum coherence and topological quantum phase transitions in the extended XY chain

We study the quantum criticality of single- and two-spin coherence, based on the quantum skew information, in the extended XY model, and analyze the impact of different driving parameters, finite temperatures and site distances of spin-pair on their critical behaviors. We find that the first-order derivative of quantum coherence can correctly detect the topological quantum phase transitions (TQPTs), but the finite temperatures strongly affect the accuracy of detection for critical points. For the case of long-distance spin-pairs, we find that the quantum coherence is a long-range correlation and its first-order derivative can also correctly detect the TQPTs at the absolute zero temperature. Moreover, the quantum coherence itself under absolute zero temperature can also signal the partial TQPTs by a local extrema in several certain situations.