  Using machine learning (ML) to recognize different phases of matter and to
infer the entire phase diagram has proven to be an effective tool given a large
dataset. In our previous proposals, we have successfully explored phase
transitions for topological phases of matter at low dimensions either in a
supervised or an unsupervised learning protocol with the assistance of quantum
information related quantities. In this work, we adopt our previous ML
procedures to study quantum phase transitions of magnetism systems such as the
XY and XXZ spin chains by using spin-spin correlation functions as the input
data. We find that our proposed approach not only maps out the phase diagrams
with accurate phase boundaries, but also indicates some new features that have
not observed before. In particular, we define so-called relevant correlation
functions to some corresponding phases that can always distinguish between
those and their neighbors. Based on the unsupervised learning protocol we
proposed [Phys. Rev. B 104, 165108 (2021)], the reduced latent representations
of the inputs combined with the clustering algorithm show the connectedness or
disconnectedness between neighboring clusters (phases), just corresponding to
the continuous or disrupt quantum phase transition, respectively.
