Detecting transition between Abelian and non-Abelian topological orders through symmetric tensor networks

We propose a unified scheme to identify phase transitions out of the Abelian topological order, including the transition to a non-Abelian chiral spin liquid. Using loop gas and and string gas states. The star lattice Kitaev model as an example, we compute the overlap of minimally entangled states through transfer matrices. We demonstrate that, similar to the anyon condensation, continuous deformation of a -injective projected entangled-pair state (PEPS) also allows us to study the transition between Abelian and non-Abelian topological orders. We show that the charge and flux anyons defined in the Abelian phase transmute into the anyon in the non-Abelian topological order. Furthermore, we show that contrary to the claim in both the LG and SG states have infinite correlation length in the non-Abelian regime, consistent with the no-go theorem that a chiral PEPS has a gapless parent Hamiltonian. ?2021 American Physical Society