Hierarchy construction for non-Abelian fractional quantum Hall states via anyon condensation

For a given parent fractional quantum Hall (FQH) state at filling fraction $\ensuremath{\nu}$, the hierarchy construction produces FQH states at nearby filling fractions ${{\ensuremath{\nu}}_n}$ by condensing minimally charged quasiholes or quasiparticles of the parent state into their own FQH states. The hierarchy construction has been useful for relating families of FQH states and for the experimental identification of the topological order of parent states via the properties of daughter states. We reinterpret the hierarchy construction as a two-step procedure: stacking with a second FQH state and condensing a condensable algebra of bosons. This two-step procedure can be applied to both Abelian and non-Abelian FQH states, and it does not require calculations with a wave function. We show this construction reproduces the hierarchies for the Laughlin and Pfaffian states, and can be applied further to propose hierarchies for various non-Abelian FQH states.