  Symmetry-protected topological (SPT) phases are short-range entangled quantum
phases with symmetry, which have gapped excitations in the bulk and gapless
modes at the edge. In this paper, we study the SPT phases in the spin-1
Heisenberg chain with a single-ion anisotropy D, which has a quantum phase
transition between a Haldane phase and a large-D phase. Using symmetric
multiscale entanglement renormalization ansatz (MERA) tensor networks, we study
the nonlocal order parameters for time-reversal and inversion symmetry. For the
inversion symmetric MERA, we propose a brick-and-rope representation that gives
a geometrical interpretation of inversion symmetric tensors. Finally, we study
the symmetric renormalization group (RG) flow of the inversion symmetric
string-order parameter, and show that entanglement renormalization with
symmetric tensors produces proper behavior of the RG fixed-points.
