  Quantifying of quantum coherence of a given system not only plays an
important role in quantum information science but also promote our
understanding on some basic problems, such as quantum phase transition.
Conventional quantum coherence measurements, such as $l_1$ norm of coherence
and relative entropy of coherence, has been widely used to study quantum phase
transition, which usually are basis-dependent. The recent quantum version of
the Jensen-Shannon divergence meet all the requirements of a good coherence
measure. It is not only a metric but also can be basis-independent. Here, based
on the quantum renormalization group method we propose an analysis on the
critical behavior of two types Ising systems when distribution of quantum
coherence. We directly obtain the trade-off relation, critical phenomena,
singular behavior, and scaling behavior for both quantum block spin system.
Furthermore, the monogamy relation in the multipartite system is also studied
in detail. These new result expand the result that quantum coherence can
decompose into various contributions as well as enlarge the applications in
using basis-independent quantum coherence to reflect quantum critical
phenomena.
