  Characterizing criticality in quantum many-body systems of dimension $\ge 2$
is one of the most important challenges of the contemporary physics. In
principle, there is no generally valid theoretical method that could solve this
problem. In this work, we propose an efficient approach to identify the
criticality of quantum systems in higher dimensions. Departing from the
analysis of the numerical renormalization group flows, we build a general
equivalence between the higher-dimensional ground state and a one-dimensional
(1D) quantum state defined in the imaginary time direction in terms of the
so-called time matrix product state (tMPS). We show that the criticality of the
targeted model can be faithfully identified by the tMPS, using the mature
scaling schemes of correlation length and entanglement entropy in 1D quantum
theories. We benchmark our proposal with the results obtained for the
Heisenberg anti-ferromagnet on honeycomb lattice. We demonstrate critical
scaling relation of the tMPS for the gapless case, and a trivial scaling for
the gapped case with spatial anisotropy. The critical scaling behaviors are
insensitive to the system size, suggesting the criticality can be identified in
small systems. Our tMPS scheme for critical scaling shows clearly that the
spin-1/2 kagom\'e Heisenberg antiferromagnet has a gapless ground state. More
generally, the present study indicates that the 1D conformal field theories in
imaginary time provide a very useful tool to characterize the criticality of
higher dimensional quantum systems.
