Non-AbelianSU(N−1)-singlet fractional quantum Hall states from coupled wires

The construction of fractional quantum Hall (FQH) states from the two-dimensional array of quantum wires provides a useful way to control strong interactions in microscopic models and has been successfully applied to the Laughlin, Moore-Read, and Read-Rezayi states. We extend this construction to the Abelian and non-Abelian $SU(N\ensuremath{-}1)$-singlet FQH states at filling fraction $\ensuremath{\nu}=k(N\ensuremath{-}1)/[N+k(N\ensuremath{-}1)m]$ labeled by integers $k$ and $m$, which are potentially realized in multicomponent quantum Hall systems or $SU(N)$ spin systems. Utilizing the bosonization approach and conformal field theory (CFT), we show that their bulk quasiparticles and gapless edge excitations are both described by an $(N\ensuremath{-}1)$-component free-boson CFT and the $SU{(N)}_k/{[U(1)]}^{N\ensuremath{-}1}$ CFT known as the Gepner parafermion. Their generalization to different filling fractions is also proposed. In addition, we argue possible applications of these results to two kinds of lattice systems: bosons interacting via occupation-dependent correlated hoppings and an $SU(N)$ Heisenberg model.