  We explore the local quantum coherence and the local quantum uncertainty,
based on Wigner-Yanase skew information, in the ground state of the anisotropic
spin-1/2 XY chain in transverse magnetic field. We show that the skew
information, as a figure of merit, supplies the necessary information to reveal
the occurrence of the second order phase transition and the completely
factorized ground state in the XY model. Additionally, in the same context, we
also discuss the usefulness of a simple experimentally friendly lower bound of
local quantum coherence. Furthermore, we demonstrate how the connection between
the appearance of non-analyticities in the local quantum uncertainty of the
ground state and the quantum phase transitions does not hold in general, by
providing explicit examples of the situation. Lastly, we discuss the ability of
the local quantum coherence to accurately estimate the critical point of the
phase transition, and investigate the robustness of the factorization
phenomenon at low temperatures.
