New perspective on the Laughlin state from classical constrain

We present a new framework of understanding the fractional quantum Hall (FQH) state at filling factor ν = n+1/3 in terms of the quasihole excitation of a different FQH state – the Gaffnian. The subspace of the Gaffnian quasiholes capture the physics at the higher Landau levels significantly better than the Laughlin state. Interestingly, this implies the fractionalisation of the Laughlin quasiholes into e/6 charges. The interactions between these charges are mediated by the Laughlin neutral excitations, which in the lowest Landau level is attractive, similar to the asymptotic freedom of quarks. However, on higher LLs, it is possible to separate these e/6 charges. This separation is linked to the softening of the quadrupole excitation that is believed to be responsible for the nematic FQH phase. The charge-e/6 quasiholes also mediate a phase transition within the same topological phase which has clear experimental signatures. We describes this phase transition in details and propose conditions for the e/6 fractional charge to be observed in experiment. Our analysis presents an application of the recently proposed local exclusion constrain (LEC) formalism, which generalizes the Jack polynomial formalism in classifying different FQH states.
Full text: https://arxiv.org/abs/2009.14214