  Recently developed tensor network methods demonstrate great potential for
addressing the quantum many-body problem, by constructing variational spaces
with polynomially, instead of exponentially, scaled parameters. Constructing
such an efficient tensor network, and thus the variational space, is a subtle
problem and the main obstacle of the method. We demonstrate the necessity of
size consistency in tensor network methods for their success in addressing the
quantum many-body problem. We further demonstrate that size consistency is
independent of the entanglement criterion, thus providing a general and tight
constraint to construct the tensor network method.
