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

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

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