New Class of Non-Abelian Spin-Singlet Quantum Hall States

We present a new class of non-Abelian spin-singlet quantum Hall states, generalizing Halperin's Abelian spin-singlet states and the Read-Rezayi non-Abelian quantum Hall states for spin-polarized electrons. We label the states by $(k,M)$ with $M$ odd (even) for fermionic (bosonic) states, and find a filling fraction $\nu =2k/(2kM+3)$. The states with $M=0\mathrm{}$ are bosonic spin-singlet states characterized by a $\mathrm{SU}(3{)}_k$ symmetry. We explain how an effective Landau-Ginzburg theory for the $\mathrm{SU}(3{)}_2$ state can be constructed. In general, the quasiparticles over these new quantum Hall states carry spin, fractional charge and non-Abelian quantum statistics.