We study the spin-1/2 star and spin-1 honeycomb Kitaev models using Z_2 invariant Projected Entangled Pair States(PEPS). We find that the transition from Abelian to non-Abelian phase of the star lattice Kitaev model can be understood as charge and flux anyons transmuting into the \sigma anyon in the Z_2 invariant PEPS framework. We show that the ground state always has infinite correlation length in the non-Abelian regime, consistent with the no-go theorem that a chiral PEPS has a gapless parent Hamiltonian. On the other hand, we confirm the Z_2 spin liquid nature of isotopic spin-1 Kitaev honeycomb model by evaluating the virtual order parameters defined on the virtual Hilbert space of the tensor network. Using the correspondence between the transfer matrix spectrum and low-lying excitations, we find that contrary to the dispersive Majorana excitation in the spin-1/2 case, the system has a dispersive charge anyon excitation. Bottom of the gapped single-particle charge anon excitations are also identified with the corresponding correlation length \xi\approx 6.7  unit cells.

[1] Yu-Hsueh Chen, Ching-Yu Huang, and Ying-Jer Kao, Phys. Rev. B 104, 045131 (2021).
[2] Yu-Hsueh Chen, Jozef Genzor, Yong Baek Kim, Ying-Jer Kao, arXiv:2107.04730 (2021).