  The power of machine learning algorithms to automatically classify different
phases of matter and detect quantum phase transitions without necessity to
characterize phases by various quantities like local order parameters or
topological invariants as in conventional approaches defined machine learning
phases of matter as a new research frontier and basic research tool in
condensed matter and statistical physics. We study quantum criticality in the
spin-1/2 square-lattice J1-J2 model with additional plaquette structure by
combination of reinforcement and supervised machine learning techniques. In our
calculations the ground-state spin-spin correlation matrices for several system
sizes are first found by restricted Boltzmann machine based variational Monte
Carlo method, equivalent to reinforcement learning, and then used as a training
data for convolutional neural network based supervised machine learning
algorithm for phases classification. The model exhibits a quantum phase
transition from paramagnetic plaquette resonating valence bond state to an
antiferromagnetic state and has been a topic of great interest because of its
close connection to cuprate superconductors and possibility of realization in
cold atoms experiments. We consider both frustrated and unfrustrated regimes
and compare our results with the results obtained previously with other
methods. We find that our results are in good agreement with the results
obtained by coupled cluster and real space renormalization group methods for
both frustrated and unfrustrated regimes. The quantum Monte Carlo and
finite-size scaling result for the unfrustrated case however slightly differs
from our result for the critical value of the inter-plaquette coupling
strength, although the results are still in reasonable agreement.
