Parton wave function for the fractional quantum Hall effect at $\nu =6\mathrm{/}17$

We consider the fractional quantum Hall effect at the filling $\nu =6\mathrm{/}17$, where experiments have observed features of incompressibility in the form of a minimum in the longitudinal resistance. We propose a parton state denoted as “$3\bar{2}{1}^3$” and show it to be a feasible candidate to capture the ground state at $\nu =6\mathrm{/}17$. We work out the low-energy effective theory of the $3\bar{2}{1}^3$ edge and make several predictions for experimentally measurable properties of the state which can help detect its underlying topological order. Intriguingly, we find that the $3\bar{2}{1}^3$ state likely lies in the same universality class as the state obtained from composite-fermionizing the 1+1/5 Laughlin state.