Symmetry protected topological (SPT) phases were first formulated in
the works of Xiao-Gang Wen and collaborators, who developed a broader
framework for understanding quantum phases beyond the traditional
Landau symmetry-breaking paradigm. These phases gained significant
attention with the discovery of topological insulators, which are
nontrivial band insulators exhibiting protected boundary states due to
time-reversal symmetry.
We have constructed SPT phases of the paramagnetic Z_3 and (Z_3)^3
Potts models. We found the Hamiltonian of the edge states, which
appears to be gapless, and we numerically calculated the central
charge of the corresponding conformal invariant theories:
c=1 for Z_3 model and c=1.72 in the (Z_3)^3 case.
We argue that at critical point they are defined by coset
SU_k(3)/SU_k(2) conformal theories at level k=1 for Z_3, and k=2
for (Z_3)^3 models, respectively.