  Determination and characterization of criticality in two-dimensional (2D)
quantum many-body systems belong to the most important challenges and problems
of quantum physics. In this paper we propose an efficient scheme to solve this
problem by utilizing the infinite projected entangled pair state (iPEPS), and
tensor network (TN) representations. We show that the criticality of a 2D state
is faithfully reproduced by the ground state (dubbed as boundary state) of a
one-dimensional effective Hamiltonian constructed from its iPEPS
representation. We demonstrate that for a critical state the correlation length
and the entanglement spectrum of the boundary state are essentially different
from those of a gapped iPEPS. This provides a solid indicator that allows to
identify the criticality of the 2D state. Our scheme is verified on the
resonating valence bond (RVB) states on kagom\'e and square lattices, where the
boundary state of the honeycomb RVB is found to be described by a $c=1$
conformal field theory. We apply our scheme also to the ground state of the
spin-1/2 XXZ model on honeycomb lattice, illustrating the difficulties of
standard variational TN approaches to study the critical ground states. Our
scheme is of high versatility and flexibility, and can be further applied to
investigate the quantum criticality in many other phenomena, such as
finite-temperature and topological phase transitions.
