Abelian origin of $\nu=2/3$ and $2+2/3$ fractional quantum Hall effect

We investigate the ground state properties of fractional quantum Hall effect at the filling factor $\nu=2/3$ and $2+2/3$, with a special focus on their typical edge physics. Via topological characterization scheme in the framework of density matrix renormalization group, the nature of $\nu=2/3$ and $2+2/3$ state are identified as Abelian hole-type Laughlin state, as evidenced by the fingerprint of entanglement spectra, central charge and topological spins. Crucially, by constructing interface between $2/3$ ($2+2/3$) state and different integer quantum Hall states, we study the structures of the interfaces from many aspects, including charge density and dipole moment. In particular, we demonstrate the edge reconstruction by visualizing edge channels comprised of two groups: the outermost $1/3$ channel and inner composite channel made of a charged mode and neutral modes.