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

Abstract

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 $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2k/(2kM+3)$. The states with $M\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ 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.