Quantum Hall states atν=2k+2: Analysis of the particle-hole conjugates of the general level-kRead-Rezayi states

Abstract

We study the $\ensuremath{\nu}=\frac{2}{k+2}$ quantum Hall states which are particle-hole conjugates of the $\ensuremath{\nu}=\frac{2}{k+2}$ Read-Rezayi states. We find that equilibration between the different modes at the edge of such a state leads to an emergent $\mathrm{SU}{(2)}_{k}$ algebra in the counter-propagating neutral sector. Heat flow along the edges of these states will be in the opposite direction of charge flow. In the $k=3$ case, which may be relevant to $\ensuremath{\nu}=2+\frac{2}{5}$, the thermal Hall conductance and the exponents associated with quasiparticle and electron tunneling distinguish this state from competing states such as the hierarchy and/or Jain state.