Topological phases of the 2D AKLT like model via study of degenerate singular value spectra

We study the two-dimensional quantum spin-3/2 systems on the honeycomb lattice, which include the 2D AKLT model. We use the infinite time-evolving block decimation (iTEBD) method to numerically solve the ground state wave function by adopting the tensor product states (TPS) ansatz. We then evaluate the singular value spectra, entanglement entropy, and the Neel order by the method of tensor renormalization group (TRG). With all these results we determine the phase diagram of the spin-3/2 model. Our result shows the singular value spectra become doubly degenerate in a belt region including the AKLT point, and indicates the existence of possible topological phases. The double degeneracy of singular value spectra is related to the recent observation in [C.-Y. Huang~and~F.-L. Lin, Phys. Rev. B 84, 125110 (2011)] of using it to characterize the topological phase. We also cross check this statement by calculating the topological Renyi entropy. The 2D AKLT state has been shown to be a universal resource for measurement-based quantum computation. Our results indicate this state is topological in nature and should be robust against local perturbations.