12:00 pm MCP 3rd Floor Atrium
Hierarchy construction for fractional quantum hall states via condensable algebras.
For a given parent fractional quantum Hall (FQH) state at filling fraction $\nu$, the hierarchy con-
struction produces FQH states at nearby filling fractions $\{\nu_n\}$ by condensing minimal 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 determining the topological orders realized in experiments. 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 wavefunction. We apply our construction to propose hierarchies for various non-abelian FQH states.