We consider the bosonic fractional quantum Hall (FQH) effect in the presence of a non-Abelian gauge field in addition to the usual Abelian magnetic field. The non-Abelian field breaks the twofold internal state degeneracy, but preserves the Landau level degeneracy. Using exact diagonalization, we find that for moderate non-Abelian field strengths the system's behaviour resembles a single internal state quantum Hall system, while for stronger fields there is a phase transition to either two internal state behaviour or the complete absence of FQH plateaus. Usually the energy gap is reduced by the presence of a non-Abelian field, but some non-Abelian fields appear to slightly increase the gap of the ν=1 and ν=3/2 Read–Rezayi states.
We investigate the disorder-driven phase transitions in bosonic fractional quantum Hall liquids at filling factors
f=1/2 and
f=1 in the lowest Landau level. We use the evolution of ground-state entanglement entropy, fidelity susceptibility, and Hall conductance with increasing disorder strength to identify the underlying phase transitions. The critical disorder strengths obtained from these different quantities are consistent with each other, validating the reliability of our numerical calculations based on exact diagonalization. At
f=1/2, we observe a clear transition from the bosonic Laughlin state to a trivial insulating phase. At
f=1, we identify a direct phase transition from the non-Abelian bosonic Moore-Read state to a trivial insulating phase, although some signs of a disorder-induced intermediate fractional quantum Hall phase were recently reported for the
f=5/2 fermionic cousin.
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.