Universal properties of the FQH state from the topological entanglement entropy and disorder effects

The topological entanglement entropy (TEE) is a robust measurement of the quantum many-body state with topological order. In fractional quantum Hall (FQH) state, it has a connection to the quantum dimension of the state itself and its quasihole excitations from the conformal field theory (CFT) description. We study the entanglement entropy (EE) in the Moore-Read (MR) and Read-Rezayi (RR) FQH states. The non-Abelian quasihole excitation induces an extra correction of the TEE which is related to its quantum dimension. With considering the effects of the disorder, the ground state TEE is stable before the spectral gap closing and the level statistics seems to have significant change with a stronger disorder, which indicates a many-body localization (MBL) transition.