From the Gaffnian critical point to the incompressible 2/5 quantum Hall state

Despite the high overlap with exact Coulomb ground state, so-called Gaffnian state fails to describe incompressibility at 2/5 quantum Hall filling factor and consequently it was conjectured be a critical state. To achieve gapped starting from wavefunction, which we interpret as inter-flavor pairing of composite fermions, propose minimally `modified Gaffnian' wavefunction keeping intact. We find that suitable hybridization these two wavefunctions is an excellent description It has very their entanglement spectra match up reasonably higher levels. Interestingly, this hybridized being representative paired suggests exotic possibility non-Abelian quasiparticle excitations filling.