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We suggest a class of two-dimensional lattice spin Hamiltonians describing non-Abelian SU(2) chiral spin liquids--spin analogs of fractional non-Abelian quantum Hall states--with gapped bulk and gapless chiral edge excitations described by the SU(2)n Wess-Zumino-Novikov-Witten conformal field theory. The models are constructed from an array of generalized spin-n/2 ladders with multi-spin-exchange interactions which are coupled by isolated spins. Such models allow a controllable analytic treatment starting from the one-dimensional limit and are characterized by a bulk gap and non-Abelian SU(2)n gapless edge excitations. [ABSTRACT FROM AUTHOR]

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-1)-singlet FQH states at filling fraction ν=k(N-1)/[N+k(N-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-1)-component free-boson CFT and the SU(N)k/[U(1)]N-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. [ABSTRACT FROM AUTHOR]

We investigate the zero-temperature phase diagram of two-orbital SU(N) fermionic models at incommensurate filling which are directly relevant to strontium and ytterbium ultracold atoms loading into a one-dimensional optical lattice. Using a low-energy approach that takes into account explicitly the SU(N) symmetry, we find that a spectral gap for the nuclear-spin degrees of freedom is formed for generic interactions. Several phases with one or two gapless modes are then stabilized which describe the competition between different density instabilities. In stark contrast to the N=2 case, no dominant pairing instabilities emerge and the leading superfluid one is rather formed from bound states of 2N fermions. [ABSTRACT FROM AUTHOR]