  We considered the question of applying the multiscale entanglement
renormalization ansatz (MERA) to describe chiral topological phases. We defined
a functional for each layer in the MERA, which captures the correlation length.
With some algebraic geometry tools, we rigorously proved its monotonicity with
respect to adjacent layers, and the existence of a lower bound for chiral
states, which shows a trade-off between the bond dimension and the correlation
length. Using this theorem, we showed the number of orbitals per cell (which
roughly corresponds to the bond dimension) should grow with the height.
Conversely, if we restrict the bond dimensions to be constant, then there is an
upper bound of the height. Specifically, we established a no-go theorem stating
that we will not approach a renormalization fixed point in this case.
