  Quantum coherence will undoubtedly play a fundamental role in understanding
of the dynamics of quantum many-body systems, thereby to reveal its genuine
contribution is of great importance. In this paper, we specialize our
discussions to the one-dimensional transverse field quantum Ising model
initialized in the coherent Gibbs state. After quenching the strength of the
transverse field, the effects of quantum coherence are studied by the rate
function of quantum work distribution. We find that quantum coherence not only
recovers the quantum phase transition destroyed by thermal fluctuations, but
also generates some entirely new singularities both in the static state and
dynamics. It can be manifested that these singularities are rooted in spin
flips causing the sudden change of the domain boundaries of spin polarization.
This work sheds new light on the fundamental connection between quantum
critical phenomena and quantum coherence.

Quantum Physics;Statistical Mechanics